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Journal articles on the topic 'Non-Cylindrical domains'

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Author: Grafiati
Published: 25 May 2024

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1

Schindlmayr, G. "Capillary Surfaces in Non-Cylindrical Domains." Zeitschrift für Analysis und ihre Anwendungen 19, no. 3 (2000): 747–62. http://dx.doi.org/10.4171/zaa/978.

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2

Jenaliyev, M. T., A. M. Serik, and M. G. Yergaliyev. "On the solvability of a boundary value problem for a two-dimensional system of Navier-Stokes equations in a cone." BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS 113, no. 1 (March 29, 2024): 84–100. http://dx.doi.org/10.31489/2024m1/84-100.

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Due to the fact that the Navier-Stokes equations are involved in the formulation of a large number of interesting problems that are important from an applied point of view, these equations have been the object of attention of mechanics, mathematicians and other scientists for several decades in a row. But despite this, many problems for the Navier-Stokes equation remain unexplored to this day. In this work, we are exploring the solvability of a boundary value problem for a two-dimensional Navier-Stokes system in a non-cylindrical degenerating domain, namely, in a cone with its vertex at the origin. Previously, we studied cases of the linearized Navier-Stokes system or non-degenerating cylindrical domains, so this work is a logical continuation of our previous research in this direction. To the above-mentioned degenerate domain we associate a family of non-degenerate truncated cones, which, in turn, are formed by a oneto-one transformation into cylindrical domains, where for the problem under consideration we established uniform a priori estimates with respect to changes in the index of the domains. Further, using a priori estimates and the Faedo-Galerkin method, we established the existence, uniqueness of solution in Sobolev classes, and its regularity as the smoothness of the given functions increases.
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3

Brown, Russell M., Wei Hu, and Gary M. Lieberman. "Weak solutions of parabolic equations in non-cylindrical domains." Proceedings of the American Mathematical Society 125, no. 6 (1997): 1785–92. http://dx.doi.org/10.1090/s0002-9939-97-03759-3.

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4

Kuliev, Komil, and Lars-Erik Persson. "An extension of Rothe’s method to non-cylindrical domains." Applications of Mathematics 52, no. 5 (October 2007): 365–89. http://dx.doi.org/10.1007/s10492-007-0021-6.

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5

Bernardi, Marco Luigi, Gianni Arrigo Pozzi, and Giuseppe Savaré. "Variational Equations of Schroedinger-Type in Non-cylindrical Domains." Journal of Differential Equations 171, no. 1 (March 2001): 63–87. http://dx.doi.org/10.1006/jdeq.2000.3834.

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6

Bran, Cristina, Jose Angel Fernandez-Roldan, Rafael P. del Real, Agustina Asenjo, Oksana Chubykalo-Fesenko, and Manuel Vazquez. "Magnetic Configurations in Modulated Cylindrical Nanowires." Nanomaterials 11, no. 3 (February 28, 2021): 600. http://dx.doi.org/10.3390/nano11030600.

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Cylindrical magnetic nanowires show great potential for 3D applications such as magnetic recording, shift registers, and logic gates, as well as in sensing architectures or biomedicine. Their cylindrical geometry leads to interesting properties of the local domain structure, leading to multifunctional responses to magnetic fields and electric currents, mechanical stresses, or thermal gradients. This review article is summarizing the work carried out in our group on the fabrication and magnetic characterization of cylindrical magnetic nanowires with modulated geometry and anisotropy. The nanowires are prepared by electrochemical methods allowing the fabrication of magnetic nanowires with precise control over geometry, morphology, and composition. Different routes to control the magnetization configuration and its dynamics through the geometry and magnetocrystalline anisotropy are presented. The diameter modulations change the typical single domain state present in cubic nanowires, providing the possibility to confine or pin circular domains or domain walls in each segment. The control and stabilization of domains and domain walls in cylindrical wires have been achieved in multisegmented structures by alternating magnetic segments of different magnetic properties (producing alternative anisotropy) or with non-magnetic layers. The results point out the relevance of the geometry and magnetocrystalline anisotropy to promote the occurrence of stable magnetochiral structures and provide further information for the design of cylindrical nanowires for multiple applications.
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7

Kubica, A., P. Rybka, and K. Ryszewska. "Weak solutions of fractional differential equations in non cylindrical domains." Nonlinear Analysis: Real World Applications 36 (August 2017): 154–82. http://dx.doi.org/10.1016/j.nonrwa.2017.01.005.

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8

Paronetto, Fabio. "An existence result for evolution equations in non-cylindrical domains." Nonlinear Differential Equations and Applications NoDEA 20, no. 6 (March 14, 2013): 1723–40. http://dx.doi.org/10.1007/s00030-013-0227-0.

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9

De Caldas, C. S. Q., J. Límaco, and R. K. Barreto. "Beam evolution equation with variable coefficients in non-cylindrical domains." Mathematical Methods in the Applied Sciences 31, no. 3 (2007): 339–61. http://dx.doi.org/10.1002/mma.912.

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10

Bottois, Arthur, Nicolae Cîndea, and Arnaud Münch. "Optimization of non-cylindrical domains for the exact null controllability of the 1D wave equation." ESAIM: Control, Optimisation and Calculus of Variations 27 (2021): 13. http://dx.doi.org/10.1051/cocv/2021010.

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This work is concerned with the null controllability of the one-dimensional wave equation over non-cylindrical distributed domains. The controllability in that case has been obtained by Castro et al. [SIAM J. Control Optim. 52 (2014)] for domains satisfying the usual geometric optic condition. We analyze the problem of optimizing the non-cylindrical support q of the control of minimal L2(q)-norm. In this respect, we prove a uniform observability inequality for a class of domains q satisfying the geometric optic condition. The proof based on the d’Alembert formula relies on arguments from graph theory. Numerical experiments are discussed and highlight the influence of the initial condition on the optimal domains.
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11

Henry, Jacques, Bento Louro, and Maria do Céu Soares. "Factorization of linear elliptic boundary value problems in non-cylindrical domains." Comptes Rendus Mathematique 349, no. 15-16 (August 2011): 879–82. http://dx.doi.org/10.1016/j.crma.2011.07.003.

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12

Ferreira, J., M. L. Santos, and M. P. Matos. "Stability for the beam equation with memory in non-cylindrical domains." Mathematical Methods in the Applied Sciences 27, no. 13 (July 23, 2004): 1493–506. http://dx.doi.org/10.1002/mma.507.

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13

Kartashov, E. M. "New energy effect in non-cylindrical domains with a thermally insulated moving boundary." Russian Technological Journal 11, no. 5 (October 6, 2023): 106–17. http://dx.doi.org/10.32362/2500-316x-2023-11-5-106-117.

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Objectives. To develop mathematical model representations of the energy effect in non-cylindrical domains having a thermally insulated moving boundary; to introduce a new boundary condition for thermal insulation of a moving boundary both for locally equilibrium heat transfer processes in the framework of classical Fourier phenomenology, as well as for more complex locally non-equilibrium processes in the framework of Maxwell–Cattaneo–Lykov–Vernott phenomenology, taking into account the finite rate of heat propagation into analytical thermophysics and applied thermomechanics; to consider an applied problem of analytical thermophysics according to the theory of thermal shock for a domain with a moving thermally insulated boundary free from external and internal influences; to obtain an exact analytical solution of the formulated mathematical models for hyperbolic type equations; to investigate the solutions obtained using a computational experiment at various values of the parameters included in it; to describe the wave nature of the kinetics of the processes under consideration.Methods. Methods and theorems of operational calculus, Riemann–Mellin contour integrals are used in calculating the originals of complex images with two branch points. A new mathematical apparatus for the equivalence of functional constructions for the originals of the obtained operational solutions, which considers the computational difficulties in finding analytical solutions to boundary value problems for equations of hyperbolic type in the domain with a moving boundary, is developed.Results. Developed mathematical models of locally nonequilibrium heat transfer and the theory of thermal shock for equations of hyperbolic type in a domain with a moving thermally insulated boundary are presented. It is shown that, despite the absence of external and internal sources of heat, the presence of a thermally insulated moving boundary leads to the appearance of a temperature gradient in the domain and, consequently, to the appearance of a temperature field and corresponding thermoelastic stresses in the domain, which have a wave character. A stochastic analysis of this energy effect forms the basis for a proposed transition of the kinetic energy of a moving thermally insulated boundary into the thermal energy of the domain. The presented model representations of the indicated effect confirmed the stated assumption.Conclusions. Mathematical models for locally nonequilibrium heat transfer processes and the theory of thermal stresses are developed and investigated on the basis of constitutive relations of the theory of thermal shock for equations of hyperbolic type in a domain with a thermally isolated moving boundary. A numerical experiment is presented to demonstrate the possibility of transiting from one form of analytical solution of a thermophysical problem to another equivalent form of a new type. The described energy effect manifests itself both for parabolic type equations based on the classical Fourier phenomenology, as well as for hyperbolic type equations based on the generalized Maxwell–Cattaneo–Lykov–Vernott phenomenology.
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14

Limaco, J., S. B. de Menezes, C. Vaz, and J. F. Montenegro. "On a Problem Connected with Navier-stokes Equations in Non Cylindrical Domains." Journal of Mathematics and Statistics 1, no. 1 (January 1, 2005): 78–85. http://dx.doi.org/10.3844/jmssp.2005.78.85.

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15

Lumer, Günter, and Roland Schnaubelt. "Time-dependent parabolic problems on non-cylindrical domains with inhomogeneous boundary conditions." Journal of Evolution Equations 1, no. 3 (September 2001): 291–309. http://dx.doi.org/10.1007/pl00001372.

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16

Cui, Lizhi, Xu Liu, and Hang Gao. "Exact controllability for a one-dimensional wave equation in non-cylindrical domains." Journal of Mathematical Analysis and Applications 402, no. 2 (June 2013): 612–25. http://dx.doi.org/10.1016/j.jmaa.2013.01.062.

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17

Antonopoulou, D. C., and M. Plexousakis. "Discontinuous Galerkin methods for the linear Schrödinger equation in non-cylindrical domains." Numerische Mathematik 115, no. 4 (March 19, 2010): 585–608. http://dx.doi.org/10.1007/s00211-010-0296-5.

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18

Argiolas, Roberto, and Anna Piro Grimaldi. "The Dirichlet problem for second order parabolic operators in non-cylindrical domains." Mathematische Nachrichten 283, no. 4 (March 18, 2010): 522–43. http://dx.doi.org/10.1002/mana.200610815.

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19

Hofmann, Steve, and John L. Lewis. "The Lp Neumann problem for the heat equation in non-cylindrical domains." Journal of Functional Analysis 220, no. 1 (March 2005): 1–54. http://dx.doi.org/10.1016/j.jfa.2004.10.016.

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20

Da Prato, G., and J. P. Zolésio. "An optimal control problem for a parabolic equation in non-cylindrical domains." Systems & Control Letters 11, no. 1 (July 1988): 73–77. http://dx.doi.org/10.1016/0167-6911(88)90114-4.

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21

Nunes, R. S. O. "On the Exact Boundary Control for the Linear Klein-Gordon Equation in Non-cylindrical Domains." TEMA (São Carlos) 21, no. 2 (July 22, 2020): 371. http://dx.doi.org/10.5540/tema.2020.021.02.371.

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The purpose of this paper is to study an exact boundary controllability problem in noncylindrical domains for the linear Klein-Gordon equation. Here, we work near of the extension techniques presented By J. Lagnese in [12] which is based in the Russell’s controllability method. The control time is obtained in any time greater then the value of the diameter of the domain on which the initial data are supported. The control is square integrable and acts on whole boundary and it is given by conormal derivative associated with the above-referenced wave operator.
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22

Antonopoulou, Dimitra, and Michael Plexousakis. "A posteriori analysis for space-time, discontinuous in time Galerkin approximations for parabolic equations in a variable domain." ESAIM: Mathematical Modelling and Numerical Analysis 53, no. 2 (March 2019): 523–49. http://dx.doi.org/10.1051/m2an/2018059.

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This paper presents an a posteriori error analysis for the discontinuous in time space–time scheme proposed by Jamet for the heat equation in multi-dimensional, non-cylindrical domains Jamet (SIAM J. Numer. Anal. 15 (1978) 913–928). Using a Clément-type interpolant, we prove abstract a posteriori error bounds for the numerical error. Furthermore, in the case of two-dimensional spatial domains we transform the problem into an equivalent one, of parabolic type, with space-time dependent coefficients but posed on a cylindrical domain. We formulate a discontinuous in time space–time scheme and prove a posteriori error bounds of optimal order. The a priori estimates of Evans (American Mathematical Society (1998)) for general parabolic initial and boundary value problems are used in the derivation of the upper bound. Our lower bound coincides with that of Picasso (Comput. Meth. Appl. Mech. Eng. 167 (1998) 223–237), proposed for adaptive, Runge-Kutta finite element methods for linear parabolic problems. Our theoretical results are verified by numerical experiments.
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23

Kawakami, Hajime, and Masaaki Tsuchiya. "Uniqueness in shape identification of a time-varying domain and related parabolic equations on non-cylindrical domains." Inverse Problems 26, no. 12 (November 2, 2010): 125007. http://dx.doi.org/10.1088/0266-5611/26/12/125007.

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24

WATANABE, Hisako. "The initial-boundary value problems for the heat operator in non-cylindrical domains." Journal of the Mathematical Society of Japan 49, no. 3 (July 1997): 399–430. http://dx.doi.org/10.2969/jmsj/04930399.

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25

Rivera-Noriega, Jorge. "Absolute continuity of parabolic measure and area integral estimates in non-cylindrical domains." Indiana University Mathematics Journal 52, no. 2 (2003): 475–524. http://dx.doi.org/10.1512/iumj.2003.52.2210.

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26

Hofmann, Steven, and John L. Lewis. "The $L^{p}$ regularity problem for the heat equation in non-cylindrical domains." Illinois Journal of Mathematics 43, no. 4 (December 1999): 752–69. http://dx.doi.org/10.1215/ijm/1256060690.

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27

Kang, Jum-Ran. "Stability for the Kirchhoff Plates Equations with Viscoelastic Boundary Conditions in Noncylindrical Domains." Abstract and Applied Analysis 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/420803.

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We study Kirchhoff plates equations with viscoelastic boundary conditions in a noncylindrical domain. This work is devoted to proving the global existence, uniqueness of solutions, and decay of the energy of solutions for Kirchhoff plates equations in a non-cylindrical domain.
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28

Antinucci, Giovanni, Alessandro Giuliani, and Rafael L. Greenblatt. "Non-integrable Ising Models in Cylindrical Geometry: Grassmann Representation and Infinite Volume Limit." Annales Henri Poincaré 23, no. 3 (October 11, 2021): 1061–139. http://dx.doi.org/10.1007/s00023-021-01107-3.

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AbstractIn this paper, meant as a companion to Antinucci et al. (Energy correlations of non-integrable Ising models: the scaling limit in the cylinder, 2020. arXiv: 1701.05356), we consider a class of non-integrable 2D Ising models in cylindrical domains, and we discuss two key aspects of the multiscale construction of their scaling limit. In particular, we provide a detailed derivation of the Grassmann representation of the model, including a self-contained presentation of the exact solution of the nearest neighbor model in the cylinder. Moreover, we prove precise asymptotic estimates of the fermionic Green’s function in the cylinder, required for the multiscale analysis of the model. We also review the multiscale construction of the effective potentials in the infinite volume limit, in a form suitable for the generalization to finite cylinders. Compared to previous works, we introduce a few important simplifications in the localization procedure and in the iterative bounds on the kernels of the effective potentials, which are crucial for the adaptation of the construction to domains with boundaries.
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29

Alkhutov, Yu A. "$ L_p$-solubility of the Dirichlet problem for the heat equation in non-cylindrical domains." Sbornik: Mathematics 193, no. 9 (October 31, 2002): 1243–79. http://dx.doi.org/10.1070/sm2002v193n09abeh000677.

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30

An Ton, Bui. "An identification problem for a time periodic nonlinear wave equation in non cylindrical domains." Nonlinear Analysis: Theory, Methods & Applications 75, no. 1 (January 2012): 182–93. http://dx.doi.org/10.1016/j.na.2011.08.020.

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31

Salvi, Rodolfo. "On the Navier-Stokes equations in non-cylindrical domains: On the existence and regularity." Mathematische Zeitschrift 199, no. 2 (June 1988): 153–70. http://dx.doi.org/10.1007/bf01159649.

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32

Guesmia, Senoussi. "Large time and space size behaviour of the heat equation in non-cylindrical domains." Archiv der Mathematik 101, no. 3 (September 2013): 293–99. http://dx.doi.org/10.1007/s00013-013-0555-7.

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33

Kheloufi, Arezki, and Boubaker-Khaled Sadallah. "On the regularity of the heat equation solution in non-cylindrical domains: Two approaches." Applied Mathematics and Computation 218, no. 5 (November 2011): 1623–33. http://dx.doi.org/10.1016/j.amc.2011.06.042.

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34

Kim, Tujin, and Daomin Cao. "Existence of solution to parabolic equations with mixed boundary condition on non-cylindrical domains." Journal of Differential Equations 265, no. 6 (September 2018): 2648–70. http://dx.doi.org/10.1016/j.jde.2018.04.046.

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35

Majewski, Pawel W., Manesh Gopinadhan, and Chinedum O. Osuji. "The Effects of Magnetic Field Alignment on Lithium Ion Transport in a Polymer Electrolyte Membrane with Lamellar Morphology." Polymers 11, no. 5 (May 15, 2019): 887. http://dx.doi.org/10.3390/polym11050887.

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The transport properties of block copolymer-derived polymer electrolyte membranes (PEMs) are sensitive to microstructural disorder originating in the randomly oriented microdomains produced during uncontrolled self-assembly by microphase separation. This microstructural disorder can negatively impact performance due to the presence of conductivity-impeding grain boundaries and the resulting tortuosity of transport pathways. We use magnetic fields to control the orientational order of Li-doped lamellar polyethylene oxide (PEO) microdomains in a liquid crystalline diblock copolymer over large length scales (>3 mm). Microdomain alignment results in an increase in the conductivity of the membrane, but the improvement relative to non-aligned samples is modest, and limited to roughly 50% in the best cases. This limited increase is in stark contrast to the order of magnitude improvement observed for magnetically aligned cylindrical microdomains of PEO. Further, the temperature dependence of the conductivity of lamellar microdomains is seemingly insensitive to the order-disorder phase transition, again in marked contrast to the behavior of cylinder-forming materials. The data are confronted with theoretical predictions of the microstructural model developed by Sax and Ottino. The disparity between the conductivity enhancements obtained by domain alignment of cylindrical and lamellar systems is rationalized in terms of the comparative ease of percolation due to the intersection of randomly oriented lamellar domains (2D sheets) versus the quasi-1D cylindrical domains. These results have important implications for the development of methods to maximize PEM conductivity in electrochemical devices, including batteries.
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36

Zhou, Feng, and Chunyou Sun. "Dynamics for the complex Ginzburg-Landau equation on non-cylindrical domains I: The diffeomorphism case." Discrete and Continuous Dynamical Systems - Series B 21, no. 10 (November 2016): 3767–92. http://dx.doi.org/10.3934/dcdsb.2016120.

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37

Zhou, Feng, Chunyou Sun, and Jiaqi Cheng. "Dynamics for the complex Ginzburg-Landau equation on non-cylindrical domains II: The monotone case." Journal of Mathematical Physics 59, no. 2 (February 2018): 022703. http://dx.doi.org/10.1063/1.5024214.

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38

Rivera-Noriega, Jorge. "Perturbation and Solvability of Initial Lp Dirichlet Problems for Parabolic Equations over Non-cylindrical Domains." Canadian Journal of Mathematics 66, no. 2 (April 1, 2014): 429–52. http://dx.doi.org/10.4153/cjm-2013-028-9.

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AbstractFor parabolic linear operators L of second order in divergence form, we prove that the solvability of initial Lp Dirichlet problems for the whole range 1 < p < ∞ is preserved under appropriate small perturbations of the coefficients of the operators involved. We also prove that if the coefficients of L satisfy a suitable controlled oscillation in the form of Carleson measure conditions, then for certain values of p > 1, the initial Lp Dirichlet problem associated with Lu = 0 over non-cylindrical domains is solvable. The results are adequate adaptations of the corresponding results for elliptic equations.
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39

Hofmann, Steve, and Kaj Nyström. "Dirichlet problems for a nonstationary linearized system of Navier–Stokes equations in non-cylindrical domains." Methods and Applications of Analysis 9, no. 1 (2002): 13–98. http://dx.doi.org/10.4310/maa.2002.v9.n1.a2.

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40

Kim, Chanwoo, and Donghyun Lee. "Decay of the Boltzmann Equation with the Specular Boundary Condition in Non-convex Cylindrical Domains." Archive for Rational Mechanics and Analysis 230, no. 1 (April 26, 2018): 49–123. http://dx.doi.org/10.1007/s00205-018-1241-5.

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41

Chowdhury, Indranil, and Prosenjit Roy. "On the asymptotic analysis of problems involving fractional Laplacian in cylindrical domains tending to infinity." Communications in Contemporary Mathematics 19, no. 05 (May 13, 2016): 1650035. http://dx.doi.org/10.1142/s0219199716500358.

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The paper is an attempt to investigate the issues of asymptotic analysis for problems involving fractional Laplacian where the domains tend to become unbounded in one-direction. Motivated from the pioneering work on second-order elliptic problems by Chipot and Rougirel in [On the asymptotic behaviour of the solution of elliptic problems in cylindrical domains becoming unbounded, Commun. Contemp. Math. 4(1) (2002) 15–44], where the force functions are considered on the cross-section of domains, we prove the non-local counterpart of their result.Recently in [Asymptotic behavior of elliptic nonlocal equations set in cylinders, Asymptot. Anal. 89(1–2) (2014) 21–35] Yeressian established a weighted estimate for solutions of non-local Dirichlet problems which exhibit the asymptotic behavior. The case when [Formula: see text] was also treated as an example to show how the weighted estimate might be used to achieve the asymptotic behavior. In this paper, we extend this result to each order between [Formula: see text] and [Formula: see text].
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42

Ortegón Gallego, F. "On distributions independent of in certain non-cylindrical domains and a de Rham lemma with a non-local constraint." Nonlinear Analysis: Theory, Methods & Applications 59, no. 3 (November 2004): 335–45. http://dx.doi.org/10.1016/j.na.2004.07.016.

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43

Cui, Y. Q., and Wei Yang. "Interplay between Fracture and Domain Switching of Ferroelectrics." Key Engineering Materials 306-308 (March 2006): 501–10. http://dx.doi.org/10.4028/www.scientific.net/kem.306-308.501.

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Applications of above-coercive electric fields lead to domain switching of a large or global scale. Large scale switching model is proposed to deal with load-induced domains witching in experiment. Both a discussion of crack initiation via the stress intensity factor and a discussion of crack path stability via T-stress are presented. The theoretical predictions and the experimental data roughly coincide for crack initiation, propagation and stability phenomena. Attention is also extended to consider the effect of non-uniform ferro-elastic domain switching in the vicinity of a crack. The domain switching zone is divided into a saturated inner core and an active surrounding annulus. Toughening for ferroelectrics with different poling states is estimated via Reuss type approximation. Solutions obtained according to spherical and cylindrical inclusions cover the range of experimental data.
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44

Cui, Lizhi, and Jing Lu. "Exact Null Controllability of a One-Dimensional Wave Equation with a Mixed Boundary." Mathematics 11, no. 18 (September 9, 2023): 3855. http://dx.doi.org/10.3390/math11183855.

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In this paper, exact null controllability of one-dimensional wave equations in non-cylindrical domains was discussed. It is different from past papers, as we consider boundary conditions for more complex cases. The wave equations have a mixed Dirichlet–Neumann boundary condition. The control is put on the fixed endpoint with a Neumann boundary condition. By using the Hilbert Uniqueness Method, exact null controllability can be obtained.
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45

Xiao, Yanping, and Chunyou Sun. "Higher-order asymptotic attraction of pullback attractors for a reaction–diffusion equation in non-cylindrical domains." Nonlinear Analysis: Theory, Methods & Applications 113 (January 2015): 309–22. http://dx.doi.org/10.1016/j.na.2014.10.012.

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46

Nazarov, S. A. "Non-self-adjoint elliptic problems with a polynomial property in domains possessing cylindrical outlets to infinity." Journal of Mathematical Sciences 101, no. 5 (October 2000): 3512–22. http://dx.doi.org/10.1007/bf02680148.

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47

Kaliev, Ibragim Adietovich, Andrei Aleksandrovich Shukhardin, and Gul'nara Sagyndykovna Sabitova. "Boundary value problems for equations of viscous heat-conducting gas in time-increasing non-cylindrical domains." Ufimskii Matematicheskii Zhurnal 6, no. 4 (2014): 81–98. http://dx.doi.org/10.13108/2014-6-4-81.

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48

Awad, Emad S. "A Note on the Spatial Decay Estimates in Non-Classical Linear Thermoelastic Semi-Cylindrical Bounded Domains." Journal of Thermal Stresses 34, no. 2 (January 13, 2011): 147–60. http://dx.doi.org/10.1080/01495739.2010.511942.

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49

Panasenko, Grigory, Konstantin Pileckas, and Bogdan Vernescu. "Steady state non-Newtonian flow with strain rate dependent viscosity in domains with cylindrical outlets to infinity." Nonlinear Analysis: Modelling and Control 26, no. 6 (November 1, 2021): 1166–99. http://dx.doi.org/10.15388/namc.2021.26.24600.

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The paper deals with a stationary non-Newtonian flow of a viscous fluid in unbounded domains with cylindrical outlets to infinity. The viscosity is assumed to be smoothly dependent on the gradient of the velocity. Applying the generalized Banach fixed point theorem, we prove the existence, uniqueness and high order regularity of solutions stabilizing in the outlets to the prescribed quasi-Poiseuille flows. Varying the limit quasi-Poiseuille flows, we prove the stability of the solution.
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ORTEGONGALLEGO, F. "On distributions independent of xNxN in certain non-cylindrical domains and a de Rham lemma with a non-local constraint." Nonlinear Analysis 59, no. 3 (November 2004): 335–45. http://dx.doi.org/10.1016/s0362-546x(04)00262-7.

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