Articles de revues : « Serrin's problem »

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Araúz, C., A. Carmona et A. M. Encinas. « Discrete Serrin's problem ». Linear Algebra and its Applications 468 (mars 2015) : 107–21. http://dx.doi.org/10.1016/j.laa.2014.01.038.

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Ciraolo, Giulio, et Rolando Magnanini. « A note on Serrin's overdetermined problem ». Kodai Mathematical Journal 37, n^o 3 (octobre 2014) : 728–36. http://dx.doi.org/10.2996/kmj/1414674618.

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Jiang, Zaihong, Li Li et Wenbo Lu. « Existence of axisymmetric and homogeneous solutions of Navier-Stokes equations in cone regions ». Discrete & ; Continuous Dynamical Systems - S 14, n^o 12 (2021) : 4231. http://dx.doi.org/10.3934/dcdss.2021126.

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In this paper, we study axisymmetric homogeneous solutions of the Navier-Stokes equations in cone regions. In [James Serrin. The swirling vortex. Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 271(1214):325-360, 1972.], Serrin studied the boundary value problem in half-space minus <inline-formula><tex-math id="M1">\begin{document}$ x_3 $\end{document}</tex-math></inline-formula>-axis, and used it to model the dynamics of tornado. We extend Serrin's work to general cone regions minus <inline-formula><tex-math id="M2">\begin{document}$ x_3 $\end{document}</tex-math></inline-formula>-axis. All axisymmetric homogeneous solutions of the boundary value problem have three possible patterns, which can be classified by two parameters. Some existence results are obtained as well.

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Magnanini, Rolando, et Giorgio Poggesi. « Serrin's problem and Alexandrov's Soap Bubble Theorem : enhanced stability via integral identities ». Indiana University Mathematics Journal 69, n^o 4 (2020) : 1181–205. http://dx.doi.org/10.1512/iumj.2020.69.7925.

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Feldman, William M. « Stability of Serrin's Problem and Dynamic Stability of a Model for Contact Angle Motion ». SIAM Journal on Mathematical Analysis 50, n^o 3 (janvier 2018) : 3303–26. http://dx.doi.org/10.1137/17m1143009.

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Magnanini, Rolando, et Giorgio Poggesi. « Interpolating estimates with applications to some quantitative symmetry results ». Mathematics in Engineering 5, n^o 1 (2022) : 1–21. http://dx.doi.org/10.3934/mine.2023002.

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<abstract>We prove interpolating estimates providing a bound for the oscillation of a function in terms of two $ L^p $ norms of its gradient. They are based on a pointwise bound of a function on cones in terms of the Riesz potential of its gradient. The estimates hold for a general class of domains, including, e.g., Lipschitz domains. All the constants involved can be explicitly computed. As an application, we show how to use these estimates to obtain stability for Alexandrov's Soap Bubble Theorem and Serrin's overdetermined boundary value problem. The new approach results in several novelties and benefits for these problems.</abstract>

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Beck, Lisa, Miroslav Bulíček et Erika Maringová. « Globally Lipschitz minimizers for variational problems with linear growth ». ESAIM : Control, Optimisation and Calculus of Variations 24, n^o 4 (octobre 2018) : 1395–413. http://dx.doi.org/10.1051/cocv/2017065.

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We study the minimization of convex, variational integrals of linear growth among all functions in the Sobolev space W1,1 with prescribed boundary values (or its equivalent formulation as a boundary value problem for a degenerately elliptic Euler–Lagrange equation). Due to insufficient compactness properties of these Dirichlet classes, the existence of solutions does not follow in a standard way by the direct method in the calculus of variations and in fact might fail, as it is well-known already for the non-parametric minimal surface problem. Assuming radial structure, we establish a necessary and sufficient condition on the integrand such that the Dirichlet problem is in general solvable, in the sense that a Lipschitz solution exists for any regular domain and all prescribed regular boundary values, via the construction of appropriate barrier functions in the tradition of Serrin’s paper [J. Serrin, Philos. Trans. R. Soc. Lond., Ser. A 264 (1969) 413–496].

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Shahgholian, Henrik. « Diversifications of Serrin's and related symmetry problems ». Complex Variables and Elliptic Equations 57, n^o 6 (juin 2012) : 653–65. http://dx.doi.org/10.1080/17476933.2010.504848.

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Ciraolo, Giulio, Rolando Magnanini et Vincenzo Vespri. « Hölder stability for Serrin’s overdetermined problem ». Annali di Matematica Pura ed Applicata (1923 -) 195, n^o 4 (8 juillet 2015) : 1333–45. http://dx.doi.org/10.1007/s10231-015-0518-7.

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Ciraolo, Giulio, et Luigi Vezzoni. « On Serrin’s overdetermined problem in space forms ». manuscripta mathematica 159, n^o 3-4 (19 octobre 2018) : 445–52. http://dx.doi.org/10.1007/s00229-018-1079-z.

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Ciraolo, Giulio, et Luigi Vezzoni. « A rigidity problem on the round sphere ». Communications in Contemporary Mathematics 19, n^o 05 (19 octobre 2016) : 1750001. http://dx.doi.org/10.1142/s0219199717500018.

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We consider a class of overdetermined problems in rotationally symmetric spaces, which reduce to the classical Serrin’s overdetermined problem in the case of the Euclidean space. We prove some general integral identities for rotationally symmetric spaces which imply a rigidity result in the case of the round sphere.

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Gálvez, José A., et Pablo Mira. « Serrin’s overdetermined problem for fully nonlinear nonelliptic equations ». Analysis & ; PDE 14, n^o 5 (22 août 2021) : 1429–42. http://dx.doi.org/10.2140/apde.2021.14.1429.

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Del Pino, Manuel, Frank Pacard et Juncheng Wei. « Serrin’s overdetermined problem and constant mean curvature surfaces ». Duke Mathematical Journal 164, n^o 14 (novembre 2015) : 2643–722. http://dx.doi.org/10.1215/00127094-3146710.

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Fall, Mouhamed Moustapha, Ignace Aristide Minlend et Tobias Weth. « Unbounded Periodic Solutions to Serrin’s Overdetermined Boundary Value Problem ». Archive for Rational Mechanics and Analysis 223, n^o 2 (12 octobre 2016) : 737–59. http://dx.doi.org/10.1007/s00205-016-1044-5.

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Nitsch, C., et C. Trombetti. « The classical overdetermined Serrin problem ». Complex Variables and Elliptic Equations 63, n^o 7-8 (8 décembre 2017) : 1107–22. http://dx.doi.org/10.1080/17476933.2017.1410798.

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Brandolini, B., C. Nitsch, P. Salani et C. Trombetti. « On the stability of the Serrin problem ». Journal of Differential Equations 245, n^o 6 (septembre 2008) : 1566–83. http://dx.doi.org/10.1016/j.jde.2008.06.010.

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Rodríguez, M. Magdalena. « A Jenkins–Serrin problem on the strip ». Journal of Geometry and Physics 57, n^o 5 (avril 2007) : 1371–77. http://dx.doi.org/10.1016/j.geomphys.2006.10.011.

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Wang, Kelei, et Juncheng Wei. « On Serrin’s overdetermined problem and a conjecture of Berestycki, Caffarelli and Nirenberg ». Communications in Partial Differential Equations 44, n^o 9 (9 mai 2019) : 837–58. http://dx.doi.org/10.1080/03605302.2019.1611846.

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Gao, Zhenghuan, Xiaohan Jia null et Jin Yan. « Serrin-Type Overdetermined Problem in $\mathbb H^n$ ». Journal of Partial Differential Equations 36, n^o 1 (juin 2023) : 102–18. http://dx.doi.org/10.4208/jpde.v36.n1.7.

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Brandolini, B., C. Nitsch, P. Salani et C. Trombetti. « Serrin-Type Overdetermined Problems : an Alternative Proof ». Archive for Rational Mechanics and Analysis 190, n^o 2 (12 août 2008) : 267–80. http://dx.doi.org/10.1007/s00205-008-0119-3.

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Bagheri, M., et Ghasem A. Afrouzi. « Multiplicity results for Kirchhoff type elliptic problems with Hardy potential ». Boletim da Sociedade Paranaense de Matemática 38, n^o 4 (10 mars 2019) : 31–50. http://dx.doi.org/10.5269/bspm.v38i4.36541.

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In this paper, we are concerned with the existence of solutions for fourth-order Kirchhoff type elliptic problems with Hardy potential. In fact, employing a consequence of the local minimum theorem due to Bonanno and mountain pass theorem we look into the existence results for the problem under algebraic conditions with the classical Ambrosetti-Rabinowitz (AR) condition on the nonlinear term. Furthermore, by combining two algebraic conditions on the nonlinear term using two consequences of the local minimum theorem due to Bonanno we ensure the existence of two solutions, applying the mountain pass theorem given by Pucci and Serrin we establish the existence of third solution for our problem.

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Gazzola, Filippo. « Critical growth problems for polyharmonic operators ». Proceedings of the Royal Society of Edinburgh : Section A Mathematics 128, n^o 2 (1998) : 251–63. http://dx.doi.org/10.1017/s0308210500012774.

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We prove that critical growth problems for polyharmonic operators admit nontrivial solutions for a wide class of lower-order perturbations of the critical term. The results highlight the phenomenon of bifurcation of the critical dimensions discovered by Pucci and Serrin; moreover, we show that another bifurcation seems to appear for ‘nonresonant’ dimensions.

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Cesari, L., et Wei H. Yang. « Serrin integrals and second order problems of plasticity ». Proceedings of the Royal Society of Edinburgh : Section A Mathematics 117, n^o 3-4 (1991) : 193–207. http://dx.doi.org/10.1017/s0308210500024677.

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SynopsisWe use the modern tools of the duality principles and the calculus of variations to formulate, analyse and solve a class of plasticity problems involving second order partial derivatives. The Serrin-type integrals can most appropriately facilitate the existence statements for the extrema from either side of the duality relation in a larger class of BV functions, and interpret the solutions with possible discontinuities on sets of measure zero. The exact solutions of a beam and numerical solutions of a circular plate are presented to demonstrate the theoretical conclusions.

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Dipierro, Serena, Giorgio Poggesi et Enrico Valdinoci. « A Serrin-type problem with partial knowledge of the domain ». Nonlinear Analysis 208 (juillet 2021) : 112330. http://dx.doi.org/10.1016/j.na.2021.112330.

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Cavallina, Lorenzo, et Toshiaki Yachimura. « On a two-phase Serrin-type problem and its numerical computation ». ESAIM : Control, Optimisation and Calculus of Variations 26 (2020) : 65. http://dx.doi.org/10.1051/cocv/2019048.

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We consider an overdetermined problem of Serrin-type with respect to an operator in divergence form with piecewise constant coefficients. We give sufficient condition for unique solvability near radially symmetric configurations by means of a perturbation argument relying on shape derivatives and the implicit function theorem. This problem is also treated numerically, by means of a steepest descent algorithm based on a Kohn–Vogelius functional.

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Cavallina, Lorenzo, Giorgio Poggesi et Toshiaki Yachimura. « Quantitative stability estimates for a two-phase Serrin-type overdetermined problem ». Nonlinear Analysis 222 (septembre 2022) : 112919. http://dx.doi.org/10.1016/j.na.2022.112919.

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Borghini, Stefano. « Symmetry results for Serrin-type problems in ring-shaped domains ». Mathematics in Engineering 5, n^o 2 (2022) : 1–16. http://dx.doi.org/10.3934/mine.2023027.

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<abstract>In this work, we employ the technique developed in [<xref ref-type="bibr" rid="b2">2</xref>] to prove rotational symmetry for a class of Serrin-type problems for the standard Laplacian. We also discuss in some length how our strategy compares with the classical moving plane method.</abstract>

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Borghini, Stefano. « Symmetry results for Serrin-type problems in ring-shaped domains ». Mathematics in Engineering 5, n^o 2 (2022) : 1–16. http://dx.doi.org/10.3934/mine.2023027.

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<abstract>In this work, we employ the technique developed in [<xref ref-type="bibr" rid="b2">2</xref>] to prove rotational symmetry for a class of Serrin-type problems for the standard Laplacian. We also discuss in some length how our strategy compares with the classical moving plane method.</abstract>

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Azzollini, Antonio. « Ground state solutions for the Hénon prescribed mean curvature equation ». Advances in Nonlinear Analysis 8, n^o 1 (14 juin 2018) : 1227–34. http://dx.doi.org/10.1515/anona-2017-0233.

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Abstract In this paper, we consider the analogous of the Hénon equation for the prescribed mean curvature problem in {{\mathbb{R}^{N}}} , both in the Euclidean and in the Minkowski spaces. Motivated by the studies of Ni and Serrin [W. M. Ni and J. Serrin, Existence and non-existence theorems for ground states for quasilinear partial differential equations, Att. Convegni Lincei 77 1985, 231–257], we have been interested in finding the relations between the growth of the potential and that of the local nonlinearity in order to prove the nonexistence of a radial ground state. We also present a partial result on the existence of a ground state solution in the Minkowski space.

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Karátson, János, Balázs Kovács et Sergey Korotov. « Discrete maximum principles for nonlinear elliptic finite element problems on surfaces with boundary ». IMA Journal of Numerical Analysis 40, n^o 2 (6 décembre 2018) : 1241–65. http://dx.doi.org/10.1093/imanum/dry086.

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AbstractThe maximum principle forms an important qualitative property of second-order elliptic equations; therefore, its discrete analogues, the so-called discrete maximum principles (DMPs), have drawn much attention owing to their role in reinforcing the qualitative reliability of the given numerical scheme. In this paper DMPs are established for nonlinear finite element problems on surfaces with boundary, corresponding to the classical pointwise maximum principles on Riemannian manifolds in the spirit of Pucci & Serrin (2007, The Maximum Principle. Springer). Various real-life examples illustrate the scope of the results.

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Zhang, Zujin, Dingxing Zhong, Shujing Gao et Shulin Qiu. « Fundamental Serrin type regularity criteria for 3D MHD fluid passing through the porous medium ». Filomat 31, n^o 5 (2017) : 1287–93. http://dx.doi.org/10.2298/fil1705287z.

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In this paper, we consider the Cauchy problem for the 3D MHD fluid passing through the porous medium, and provide some fundamental Serrin type regularity criteria involving the velocity or its gradient, the pressure or its gradient. This extends and improves [S. Rahman, Regularity criterion for 3D MHD fluid passing through the porous medium in terms of gradient pressure, J. Comput. Appl. Math., 270 (2014), 88-99].

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Esposito, Francesco, et Berardino Sciunzi. « The Moving Plane Method for Doubly Singular Elliptic Equations Involving a First-Order Term ». Advanced Nonlinear Studies 21, n^o 4 (27 octobre 2021) : 905–16. http://dx.doi.org/10.1515/ans-2021-2151.

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Abstract In this paper we deal with positive singular solutions to semilinear elliptic problems involving a first-order term and a singular nonlinearity. Exploiting a fine adaptation of the well-known moving plane method of Alexandrov–Serrin and a careful choice of the cutoff functions, we deduce symmetry and monotonicity properties of the solutions.

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Li, Hao, et Yachun Li. « Local existence and Serrin-type blow-up criterion for strong solutions to the radiation hydrodynamic equations ». Journal of Hyperbolic Differential Equations 17, n^o 03 (septembre 2020) : 501–57. http://dx.doi.org/10.1142/s0219891620500149.

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We consider the Cauchy problem for the three-dimensional, compressible radiation hydrodynamic equations. We establish the existence and uniqueness of local strong solutions for large initial data satisfying some compatibility condition. The initial density need not be positive and may vanish in an open set. Moreover, we establish a Serrin-type blow-up criterion, which is stated in terms of the velocity and density variables [Formula: see text] and is independent of the temperature and the radiation intensity.

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Fernández-Rincón, Sergio, et Julián López-Gómez. « The Singular Perturbation Problem for a Class of Generalized Logistic Equations Under Non-classical Mixed Boundary Conditions ». Advanced Nonlinear Studies 19, n^o 1 (1 février 2019) : 1–27. http://dx.doi.org/10.1515/ans-2018-2034.

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Abstract This paper studies a singular perturbation result for a class of generalized diffusive logistic equations, {d\mathcal{L}u=uh(u,x)} , under non-classical mixed boundary conditions, {\mathcal{B}u=0} on {\partial\Omega} . Most of the precursors of this result dealt with Dirichlet boundary conditions and self-adjoint second order elliptic operators. To overcome the new technical difficulties originated by the generality of the new setting, we have characterized the regularity of {\partial\Omega} through the regularity of the associated conormal projections and conormal distances. This seems to be a new result of a huge relevance on its own. It actually complements some classical findings of Serrin, [39], Gilbarg and Trudinger, [21], Krantz and Parks, [27], Foote, [18] and Li and Nirenberg [28] concerning the regularity of the inner distance function to the boundary.

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Kang, Hyeonbae, et Shigeru Sakaguchi. « A symmetry theorem in two-phase heat conductors ». Mathematics in Engineering 5, n^o 3 (2022) : 1–7. http://dx.doi.org/10.3934/mine.2023061.

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<abstract>We consider the Cauchy problem for the heat diffusion equation in the whole Euclidean space consisting of two media with different constant conductivities, where initially one medium has temperature 0 and the other has temperature 1. Under the assumptions that one medium is bounded and the interface is of class $ C^{2, \alpha} $, we show that if the interface is stationary isothermic, then it must be a sphere. The method of moving planes due to Serrin is directly utilized to prove the result.</abstract>

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Crasta, Graziano, et Ilaria Fragalà. « On the Dirichlet and Serrin Problems for the Inhomogeneous Infinity Laplacian in Convex Domains : Regularity and Geometric Results ». Archive for Rational Mechanics and Analysis 218, n^o 3 (20 mai 2015) : 1577–607. http://dx.doi.org/10.1007/s00205-015-0888-4.

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Gazzola, Filippo, et Gianmarco Sperone. « Remarks on radial symmetry and monotonicity for solutions of semilinear higher order elliptic equations ». Mathematics in Engineering 4, n^o 5 (2021) : 1–24. http://dx.doi.org/10.3934/mine.2022040.

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<abstract>Half a century after the appearance of the celebrated paper by Serrin about overdetermined boundary value problems in potential theory and related symmetry properties, we reconsider semilinear polyharmonic equations under Dirichlet boundary conditions in the unit ball of $ \mathbb{R}^{n} $. We discuss radial properties (symmetry and monotonicity) of positive solutions of such equations and we show that, in <italic>conformal dimensions</italic>, the associated Green function satisfies elegant reflection and symmetry properties related to a suitable Kelvin transform (inversion about a sphere). This yields an alternative formula for computing the partial derivatives of solutions of polyharmonic problems. Moreover, it gives some hints on how to modify a counterexample by Sweers where radial monotonicity fails: we numerically recover strict radial monotonicity for the biharmonic equation in the unit ball of $ \mathbb{R}^{4} $.</abstract>

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A.A., Shlapunov, et Tarkhanov N.N. « Inverse image of precompact sets and regular solutions to the Navier–Stokes equations ». Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki 32, n^o 2 (juin 2022) : 278–97. http://dx.doi.org/10.35634/vm220208.

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We consider the initial value problem for the Navier–Stokes equations over ${\mathbb R}^3 \times [0,T]$ with time $T>0$ in the spatially periodic setting. We prove that it induces open injective mappings ${\mathcal A}_s\colon B^{s}_1 \to B^{s-1}_2$ where $B^{s}_1$, $B^{s-1}_2$ are elements from scales of specially constructed function spaces of Bochner–Sobolev type parametrized with the smoothness index $s \in \mathbb N$. Finally, we prove that a map ${\mathcal A}_s$ is surjective if and only if the inverse image ${\mathcal A}_s ^{-1}(K)$ of any precompact set $K$ from the range of the map ${\mathcal A}_s$ is bounded in the Bochner space $L^{\mathfrak s} ([0,T], L^{{\mathfrak r}} ({\mathbb T}^3))$ with the Ladyzhenskaya–Prodi–Serrin numbers ${\mathfrak s}$, ${\mathfrak r}$.

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VITILLARO, ENZO. « ON THE LAPLACE EQUATION WITH NON-LINEAR DYNAMICAL BOUNDARY CONDITIONS ». Proceedings of the London Mathematical Society 93, n^o 2 (7 août 2006) : 418–46. http://dx.doi.org/10.1112/s0024611506015875.

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The main part of the paper deals with local existence and global existence versus blow-up for solutions of the Laplace equation in bounded domains with a non-linear dynamical boundary condition. More precisely, we study the problem consisting in: (1) the Laplace equation in $(0, \infty) \times \Omega$; (2) a homogeneous Dirichlet condition $(0, \infty) \times \Gamma_0$; (3) the dynamical boundary condition $ \frac {\partial u}{\partial \nu} = - |u_t|^{m-2} u_t + |u|^{p - 2} u$ on $(0, \infty) \times \Gamma_1$; (4) the initial condition $u(0, x) = u_0 (x)$ on $\partial \Omega$. Here $\Omega$ is a regular and bounded domain in $\mathbb{R}^n$, with $n \ge 1$, and $\Gamma_0$ and $\Gamma_1$ endow a measurable partition of $\partial \Omega$. Moreover, $m>1$, $2 \le p < r$, where $r = 2 (n - 1) / (n - 2)$ when $n \ge 3$, $r = \infty$ when $n = 1,2$, and $u_0 \in H^{1/2} (\partial \Omega)$, $u_0 = 0$ on $\Gamma_0$.The final part of the paper deals with a refinement of a global non-existence result by Levine, Park and Serrin, which is applied to the previous problem.

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Hedrih-Stevanovic, Katica. « Advances in classical and analytical mechanics : A reviews of author’s results ». Theoretical and Applied Mechanics 40, n^o 2 (2013) : 293–383. http://dx.doi.org/10.2298/tam1302293h.

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A review, in subjective choice, of author?s scientific results in area of: classical mechanics, analytical mechanics of discrete hereditary systems, analytical mechanics of discrete fractional order system vibrations, elastodynamics, nonlinear dynamics and hybrid system dynamics is presented. Main original author?s results were presented through the mathematical methods of mechanics with examples of applications for solving problems of mechanical real system dynamics abstracted to the theoretical models of mechanical discrete or continuum systems, as well as hybrid systems. Paper, also, presents serries of methods and scientific results authored by professors Mitropolyski, Andjelic and Raskovic, as well as author?s of this paper original scientific research results obtained by methods of her professors. Vector method based on mass inertia moment vectors and corresponding deviational vector components for pole and oriented axis, defined in 1991 by K. Hedrih, is presented. Results in construction of analytical dynamics of hereditary discrete system obtained in collaboration with O. A. Gorosho are presented. Also, some selections of results author?s postgraduate students and doctorantes in area of nonlinear dynamics are presented. A list of scientific projects headed by author of this paper is presented with a list of doctoral dissertation and magister of sciences thesis which contain scientific research results obtained under the supervision by author of this paper or their fist doctoral candidates.

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Saeed, Faisal, Haider Ali Tauqeer, Hasan Erteza Gelani, Muhammad Hassan Yousuf et Asad Idrees. « Numerical modeling, simulation and evaluation of conventional and hybrid photovoltaic modules interconnection configurations under partial shading conditions ». EPJ Photovoltaics 13 (2022) : 10. http://dx.doi.org/10.1051/epjpv/2022004.

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Partial shading on solar photovoltaic (PV) arrays is a prevalent problem in photovoltaic systems that impair the performance of PV modules and is responsible for reduced power output as compared to that in standard irradiance conditions thereby resulting in the appearance of multiple maximas on panel output power characteristics. These maxims contribute to mismatch power losses among PV modules. The mismatch losses depend on shading characteristics together with different interconnected configuration schemes of PV modules. The research presents a comparative analysis of partial shading effects on a 4 × 4 PV array system connected in series (S), parallel (P), serries-parallel (SP), total-cross-tied (TCT), central-cross-tied (CCT), bridge-linked (BL), bridge-linked total cross-tied (BLTCT), honey-comb (HC), honey-comb total-cross-tied (HCTCT) and ladder (LD) configurations using MATLAB/Simulink. The PV module SPR-X20-250-BLK was used for modeling and simulation analysis. Each module is comprised of 72 number of PV cells and a combination of 16 PV modules was employed for the contextual analysis. Accurate mathematical modeling for the HCTCT configuration under partial shading conditions (PSCs) is provided for the first time and is verified from the simulation. The different configuration schemes were investigated under short-narrow, short-wide, long-narrow, long-wide, diagonal, entire row distribution, and entire column distribution partial shading condition patterns with mathematical implementation and simulation of passing clouds. The performance of array configurations is compared in terms of maximum power generated (Pmp), mismatch power loss (ΔPml), relative power loss (Prl) and the fill factor (FF). It was inferred that on average, TCT configuration yielded maximum power generation under all shading patterns among all PV modules interconnection configurations with minimum mismatch power losses followed by hybrid and conventional PV array configurations respectively.

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Irawati, Wahyu. « Potensi Mikroorganisme Resisten dari Pantai Timur Surabaya Sebagai Biosorben Seng ». JURNAL BIOLOGI PAPUA 11, n^o 2 (31 octobre 2019) : 80–86. http://dx.doi.org/10.31957/jbp.878.

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East coast of Surabaya is one of region in Indonesia which contaminated by heavy metals, such as zinc. Zinc is one of essential heavy metals for organisms but be dangerous for human if comsumed in high concentration. So, it is important to to solve the problem to reduce the concentration of zinc in east coast of Surabaya through bioremediation using microorganism. Zinc resistant microorganism could be isolated from zinc contaminated region and be used for bioremediation agent because some microorganism developed resistance mechanism to zinc by bioaccumulation or biosorption. The aims of this study are to isolate and characterize zinc resistant microorganism from east coast of Surabaya. The most resistant microorganism will be observed for the growth in medium supplemented with zinc and without zinc. The potency of the chosen isolate to biosorb of zinc was also analyzed. Water sample from east coast of Surabaya was serries dilluted and innoculated on Luria Bertani Agar medium using spread plated method. Microbial resistance to zinc was analyzed by grown the cell on medium containing various concentration of zinc to determine Minimum Inhibitory Concentration (MIC) value of each microbial isolate. Cell turbidity will be observed in the chosen isolate using spectrophotometer in wave length of 600 nm to get the growth curve. The potency of the chosen isolate to biosorb of zinc was analyzed using atomic absorption spectrophotometer. From this study, six bacteria and three yeast have been isolated from east coast of Surabaya, designated as PmbZn1, PmbZn2, PmbZn3, PmbZn4, PmbZn5, PmbZn6, PmbZn7, PmbZn8, dan PmbZn9. All isolates could grow on medium containing 8 mM ZnSO4. The most resistant bacterial was isolate PmbZn5 with the MIC of 9 mM ZnSO4. The potency of the isolate to biosorb of zinc was 94,79 and 93,57% in medium containing 4 mM and 7 mM ZnSO4, respectively.Key words: Bacteria, biosorb, resistant, yeast, zinc.

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Yau, Pun Wong, Shixiao Wang et Zvi Rusak. « Extension to nonlinear stability theory of the circular Couette flow ». Journal of Fluid Mechanics 795 (19 avril 2016) : 455–93. http://dx.doi.org/10.1017/jfm.2016.219.

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A nonlinear stability analysis of the viscous circular Couette flow to axisymmetric finite-amplitude perturbations under axial periodic boundary conditions is developed. The analysis is based on investigating the properties of a reduced Arnol’d energy-Casimir function $\mathscr{A}_{rd}$ of Wang (Phys. Fluids, vol. 2, 2009, 084104). A weighted kinetic energy of the perturbation, which has a form of ${\rm\Delta}\mathscr{A}_{rd}$, the difference between the reduced Arnol’d function and its base flow value, is used as a Lyapunov function. We show that all the inviscid flow effects as well as all the viscous-dependent terms that are related to the flow boundaries vanish. The evolution of ${\rm\Delta}\mathscr{A}_{rd}$ depends only on the viscous effects of the perturbation’s dynamics inside the flow domain. The requirement for the temporal decay of ${\rm\Delta}\mathscr{A}_{rd}$ leads to two novel sufficient conditions for the nonlinear stability of the circular Couette flow in response to axisymmetric perturbations. The linearized version of these conditions for infinitesimally small perturbations recovers the recent linear stability results by Kloosterziel (J. Fluid Mech., vol. 652, 2010, pp. 171–193). By examining the nonlinear stability conditions, we establish a definite operational region of the viscous circular Couette flow that is independent of the fluid viscosity. In this region of operation, the flow is nonlinearly stable in response to perturbations of any size, provided that the initial total circulation function is above a minimum level determined by the operational conditions of the base flow. Comparisons with historical studies show that our results shed light on the experimental measurements of Wendt (Ing.-Arch., vol. 4, 1933, pp. 577–595) and extend the classical nonlinear stability results of Serrin (Arch. Rat. Mech. Anal., vol. 3, 1959, pp. 1–13) and Joseph & Hung (Arch. Rat. Mech. Anal., vol. 44, 1971, pp. 1–22). When the flow is nonlinearly stable and evolves axisymmetrically for all time, then it always decays asymptotically in time to the circular Couette flow determined uniquely by the set-up of the rotating cylinders. Finally, we derive upper-bound estimates on the decay rate of finite-amplitude perturbations for the solid-body rotation flow between two coaxial rotating cylinders and for the circular Couette flow. We demonstrate via numerical simulations that the theoretical upper bound is relevant to the dynamics of various axisymmetric perturbations tested, where it is strictly obeyed. This present study provides new physical insights into a classical flow problem that was studied for many decades.

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Fall, Mouhamed Moustapha, et Ignace Aristide Minlend. « Serrin's over-determined problem on Riemannian manifolds ». Advances in Calculus of Variations 8, n^o 4 (1 janvier 2015). http://dx.doi.org/10.1515/acv-2014-0017.

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Kamburov, Nikola, et Luciano Sciaraffia. « Nontrivial solutions to Serrin's problem in annular domains ». Annales de l'Institut Henri Poincaré C, Analyse non linéaire, mai 2020. http://dx.doi.org/10.1016/j.anihpc.2020.05.001.

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Farina, Alberto, et Alberto Roncoroni. « Serrin’s type problems in warped product manifolds ». Communications in Contemporary Mathematics, 16 mars 2021, 2150020. http://dx.doi.org/10.1142/s0219199721500206.

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In this paper, we consider Serrin’s overdetermined problems in warped product manifolds and we prove Serrin’s type rigidity results by using the [Formula: see text]-function approach introduced by Weinberger.

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Fall, Mouhamed Moustapha, Ignace Aristide Minlend et Tobias Weth. « Serrin’s overdetermined problem on the sphere ». Calculus of Variations and Partial Differential Equations 57, n^o 1 (13 novembre 2017). http://dx.doi.org/10.1007/s00526-017-1275-9.

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Ciraolo, Giulio, et Alberto Roncoroni. « Serrin’s type overdetermined problems in convex cones ». Calculus of Variations and Partial Differential Equations 59, n^o 1 (9 janvier 2020). http://dx.doi.org/10.1007/s00526-019-1678-x.

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Scheuer, Julian, et Chao Xia. « Stability for Serrin’s Problem and Alexandroff’s Theorem in Warped Product Manifolds ». International Mathematics Research Notices, 21 octobre 2022. http://dx.doi.org/10.1093/imrn/rnac294.

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Abstract We prove quantitative versions for several results from geometric partial differential equations. Firstly, we obtain a double stability theorem for Serrin’s overdetermined problem in spaceforms. Secondly, we prove stability theorems for Brendle’s Heintze–Karcher inequality respectively constant mean curvature classification in a class of warped product spaces. The key tool is the first author’s recent development of stability for level sets of a function under smallness of the traceless Hessian thereof.

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Magnanini, Rolando, et Giorgio Poggesi. « Nearly optimal stability for Serrin’s problem and the Soap Bubble theorem ». Calculus of Variations and Partial Differential Equations 59, n^o 1 (18 janvier 2020). http://dx.doi.org/10.1007/s00526-019-1689-7.

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