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Journal articles on the topic 'Oblique boundary value problem'

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Published: 4 June 2021

Last updated: 28 January 2023

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1

Turmetov, Batirkhan, Maira Koshanova, and Moldir Muratbekova. "On some analogues of periodic problems for Laplace equation with an oblique derivative under boundary conditions." e-Journal of Analysis and Applied Mathematics 2020, no. 1 (January 1, 2020): 13–27. http://dx.doi.org/10.2478/ejaam-2020-0002.

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AbstractIn this paper, we study solvability of new classes of nonlocal boundary value problems for the Laplace equation in a ball. The considered problems are multidimensional analogues (in the case of a ball) of classical periodic boundary value problems in rectangular regions. To study the main problem, first, for the Laplace equation, we consider an auxiliary boundary value problem with an oblique derivative. This problem generalizes the well-known Neumann problem and is conditionally solvable. The main problems are solved by reducing them to sequential solution of the Dirichlet problem and the problem with an oblique derivative. It is proved that in the case of periodic conditions, the problem is conditionally solvable; and in this case the exact condition for solvability of the considered problem is found. When boundary conditions are specified in the anti-periodic conditions form, the problem is certainly solvable. The obtained general results are illustrated with specific examples.

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2

Nazarova, Kulzina Zh, Batirkhan Kh Turmetov, and Kairat Id Usmanov. "On a nonlocal boundary value problem with an oblique derivative." Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva 22, no. 1 (March 31, 2020): 81–93. http://dx.doi.org/10.15507/2079-6900.22.202001.81-93.

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The work studies the solvability of a nonlocal boundary value problem for the Laplace equation. The nonlocal condition is introduced using transformations in the Rn space carried out by some orthogonal matrices. Examples and properties of such matrices are given. To study the main problem, an auxiliary nonlocal Dirichlet-type problem for the Laplace equation is first solved. This problem is reduced to a vector equation whose elements are the solutions of the classical Dirichlet probem. Under certain conditions for the boundary condition coefficients, theorems on uniqueness and existence of a solution to a problem of Dirichlet type are proved. For this solution an integral representation is also obtained, which is a generalization of the classical Poisson integral. Further, the main problem is reduced to solving a non-local Dirichlet-type problem. Theorems on existence and uniqueness of a solution to the problem under consideration are proved. Using well-known statements about solutions of a boundary value problem with an oblique derivative for the classical Laplace equation, exact orders of smoothness of a problem's solution are found. Examples are also given of the cases where the theorem conditions are not fulfilled. In these cases the solution is not unique.

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3

Nazarov, A. I., and N. N. Uraltseva. "The oblique boundary-value problem for a quasilinear parabolic equation." Journal of Mathematical Sciences 77, no. 3 (November 1995): 3212–20. http://dx.doi.org/10.1007/bf02364713.

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4

Bauer, Frank. "Split operators for oblique boundary value problems." Applicable Analysis 87, no. 1 (January 2008): 45–57. http://dx.doi.org/10.1080/00036810701603029.

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5

Díaz, G., J. I. Díaz, and J. Otero. "On an oblique boundary value problem related to the Backus problem in Geodesy." Nonlinear Analysis: Real World Applications 7, no. 2 (April 2006): 147–66. http://dx.doi.org/10.1016/j.nonrwa.2005.01.001.

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6

Borsuk, Mikhail. "Boundary value problems for singular p- and p(x)- Laplacian equations in a domain with conical point on the boundary." Ukrainian Mathematical Bulletin 17, no. 4 (December 13, 2020): 455–83. http://dx.doi.org/10.37069/1810-3200-2020-17-4-1.

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This paper is a survey of our last results about solutions to the Dirichlet and Robin boundary problems, the Robin transmission problem for an elliptic quasilinear second-order equation with the constant p- and variable p(x)-Laplacians, as well as to the degenerate oblique derivative problem for elliptic linear and quasilinear second-order equations in a conical bounded n-dimensional domain.

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7

Macák, Marek, Zuzana Minarechová, and Karol Mikula. "A novel scheme for solving the oblique derivative boundary-value problem." Studia Geophysica et Geodaetica 58, no. 4 (May 8, 2014): 556–70. http://dx.doi.org/10.1007/s11200-013-0340-x.

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8

Doumic, Marie. "Boundary Value Problem for an Oblique Paraxial Model of Light Propagation." Methods and Applications of Analysis 16, no. 1 (2009): 119–38. http://dx.doi.org/10.4310/maa.2009.v16.n1.a7.

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9

Gutting, Martin. "Fast multipole accelerated solution of the oblique derivative boundary value problem." GEM - International Journal on Geomathematics 3, no. 2 (May 30, 2012): 223–52. http://dx.doi.org/10.1007/s13137-012-0038-1.

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10

Jiang, Feida, Neil S. Trudinger, and Ni Xiang. "On the Neumann Problem for Monge-Ampére Type Equations." Canadian Journal of Mathematics 68, no. 6 (December 1, 2016): 1334–61. http://dx.doi.org/10.4153/cjm-2016-001-3.

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AbstractIn this paper, we study the global regularity for regular Monge-Ampère type equations associated with semilinear Neumann boundary conditions. By establishing a priori estimates for second order derivatives, the classical solvability of the Neumann boundary value problem is proved under natural conditions. The techniques build upon the delicate and intricate treatment of the standard Monge-Ampère case by Lions, Trudinger, and Urbas in 1986 and the recent barrier constructions and second derivative bounds by Jiang, Trudinger, and Yang for the Dirichlet problem. We also consider more general oblique boundary value problems in the strictly regular case.

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11

Jiang, Feida, and Neil S. Trudinger. "Oblique boundary value problems for augmented Hessian equations III." Communications in Partial Differential Equations 44, no. 8 (April 14, 2019): 708–48. http://dx.doi.org/10.1080/03605302.2019.1597113.

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12

Lieberman, Gary M., and Neil S. Trudinger. "Nonlinear oblique boundary value problems for nonlinear elliptic equations." Transactions of the American Mathematical Society 295, no. 2 (February 1, 1986): 509. http://dx.doi.org/10.1090/s0002-9947-1986-0833695-6.

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13

Jiang, Feida, and Neil S. Trudinger. "Oblique boundary value problems for augmented Hessian equations II." Nonlinear Analysis: Theory, Methods & Applications 154 (May 2017): 148–73. http://dx.doi.org/10.1016/j.na.2016.08.007.

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14

Jiang, Feida, and Neil S. Trudinger. "Oblique boundary value problems for augmented Hessian equations I." Bulletin of Mathematical Sciences 8, no. 2 (May 21, 2018): 353–411. http://dx.doi.org/10.1007/s13373-018-0124-2.

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15

Mehats, Florian. "Convergence of a numerical scheme for a nonlinear oblique derivative boundary value problem." ESAIM: Mathematical Modelling and Numerical Analysis 36, no. 6 (November 2002): 1111–32. http://dx.doi.org/10.1051/m2an:2003008.

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16

Macák, Marek, Zuzana Minarechová, Róbert Čunderlík, and Karol Mikula. "The Finite Element Method as a Tool to Solve the Oblique Derivative Boundary Value Problem in Geodesy." Tatra Mountains Mathematical Publications 75, no. 1 (April 1, 2020): 63–80. http://dx.doi.org/10.2478/tmmp-2020-0005.

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AbstractIn this paper, we propose a novel approach to approximate the solution of the Laplace equation with an oblique derivative boundary condition by the finite element method. We present and analyse diverse testing experiments to study its behaviour and convergence. Finally, the usefulness of this approach is demonstrated by using it to gravity field modelling, namely, to approximate the solution of a geodetic boundary value problem in Himalayas.

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17

Kopaev, A. V. "Oblique Derivative Problem Solution for the Lavrentyev-Bitsadze Equation in a Half-Plane." Mathematics and Mathematical Modeling, no. 6 (January 15, 2019): 1–10. http://dx.doi.org/10.24108/mathm.0618.0000149.

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The paper solves the boundary value problem of an oblique derivative for the Lavrent'ev – Bitsadze equation in a half-plane. The Lavrent'ev – Bitsadze equation is an equation of mixed (elliptic-hyperbolic) type. Mixed-type equations arise when solving many applied problems (for example, when simulating transonic flows of a compressible medium).In the paper, the domain of ellipticity is a half-plane, and that of hyperbolicity is its adjacent strip. On one of the straight lines bounding the strip, an oblique derivative is specified (in the direction that forms an acute angle with this straight line), and on the other straight line, which is the interface between the strip and the half-plane, the solutions are matched by boundary conditions of the fourth kind. In the hyperbolicity strip, the solution is represented by the d'Alembert formula, and in the half-plane, where the equation is elliptic, the bounded solution is represented by the Poisson integral with unknown density. For this unknown density of the Poisson integral, a singular integral equation is obtained, which is reduced to the Riemann boundary value problem with a shift for holomorphic functions. The solution of the Riemann problem is reduced to the solution of two functional equations. Solutions of these functional equations and the Sokhotsky formula for an integral of Cauchy type allowed us to find the unknown density of the Poisson integral. This allowed us to find a solution to the oblique derivative problem as the sum of a functional series (up to an arbitrary constant term).

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18

Gramchev, T. V., and P. R. Popivanov. "Airy operators and singular oblique derivative diffractive boundary value problems." Communications in Partial Differential Equations 11, no. 10 (January 1986): 1009–30. http://dx.doi.org/10.1080/03605308608820455.

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19

Hsu, Pei. "Asymptotic behavior of solutions of oblique derivative boundary value problems." Michigan Mathematical Journal 36, no. 2 (1989): 221–44. http://dx.doi.org/10.1307/mmj/1029003945.

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20

Benseridi, Hamid, and Mourad Dilmi. "Nonlinear and oblique boundary value problems for the Stokes equations." Electronic Journal of Qualitative Theory of Differential Equations, no. 82 (2011): 1–8. http://dx.doi.org/10.14232/ejqtde.2011.1.82.

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21

RAMKRISHNA, DORAISWAMI, and NEAL R. AMUNDSON. "MORE ON OBLIQUE AND MIXED, SECOND DERIVATIVE BOUNDARY VALUE PROBLEMS." Chemical Engineering Communications 58, no. 1-6 (August 1987): 397–411. http://dx.doi.org/10.1080/00986448708911978.

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22

Urbas, John. "Oblique boundary value problems for equations of Monge-Ampère type." Calculus of Variations and Partial Differential Equations 7, no. 1 (June 1, 1998): 19–39. http://dx.doi.org/10.1007/s005260050097.

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23

Li, Song-Ying. "On the oblique boundary value problems for Monge-Ampère equations." Pacific Journal of Mathematics 190, no. 1 (September 1, 1999): 155–72. http://dx.doi.org/10.2140/pjm.1999.190.155.

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24

CHAKRABORTY, RUMPA, and B. N. MANDAL. "OBLIQUE WAVE SCATTERING BY A RECTANGULAR SUBMARINE TRENCH." ANZIAM Journal 56, no. 3 (January 2015): 286–98. http://dx.doi.org/10.1017/s1446181115000024.

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The problem of oblique wave scattering by a rectangular submarine trench is investigated assuming a linearized theory of water waves. Due to the geometrical symmetry of the rectangular trench about the central line $x=0$, the boundary value problem is split into two separate problems involving the symmetric and antisymmetric potential functions. A multi-term Galerkin approximation involving ultra-spherical Gegenbauer polynomials is employed to solve the first-kind integral equations arising in the mathematical analysis of the problem. The reflection and transmission coefficients are computed numerically for various values of different parameters and different angles of incidence of the wave train. The coefficients are depicted graphically against the wave number for different situations. Some curves for these coefficients available in the literature and obtained by different methods are recovered.

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25

Popivanov, P. R., and D. K. Palagachev. "Boundary value problem with a tangential oblique derivative for second order quasilinear elliptic operators." Nonlinear Analysis: Theory, Methods & Applications 21, no. 2 (July 1993): 123–30. http://dx.doi.org/10.1016/0362-546x(93)90042-q.

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26

Urbas, John. "Nonlinear oblique boundary value problems for Hessian equations in two dimensions." Annales de l'Institut Henri Poincare (C) Non Linear Analysis 12, no. 5 (September 1995): 507–75. http://dx.doi.org/10.1016/s0294-1449(16)30150-0.

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27

Garroni, M. G., V. A. Solonnikov, and M. A. Vivaldi. "Existence and regularity results for oblique derivative problems for heat equations in an angle." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 128, no. 1 (1998): 47–79. http://dx.doi.org/10.1017/s0308210500027153.

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An initial-boundary-value problem is considered for the heat equation in an infinite angle dθr ⊆ R2 × [0, ∞) with the oblique derivative boundary conditions on the faces λi of the angle:with either h0 + h1 > 0, or h0 + h1 ≦ 0. The unique solvability of such a problem is proved in appropriate weighted Sobolev spaces according to the sign of h0 + h1. Estimates of the solution are obtained under ‘natural’ restrictions on the opening of the angle.

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28

Mehats, Florian, and Jean-Michel Roquejoffre. "A nonlinear oblique derivative boundary value problem for the heat equation Part 1: Basic results." Annales de l'Institut Henri Poincare (C) Non Linear Analysis 16, no. 2 (March 1999): 221–53. http://dx.doi.org/10.1016/s0294-1449(99)80013-4.

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29

Manam, S. R., J. Bhattacharjee, and T. Sahoo. "Expansion formulae in wave structure interaction problems." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 462, no. 2065 (November 11, 2005): 263–87. http://dx.doi.org/10.1098/rspa.2005.1562.

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A large class of problems in the field of fluid–structure interaction involves higher-order boundary conditions for the governing partial differential equation and the eigenfunctions associated with these problems are not orthogonal in the usual sense. In the present study, mode-coupling relations are derived by utilizing the Fourier integral theorem for the solutions of the Laplace equation with higher-order derivatives in the boundary conditions in both the cases of a semi-infinite strip and a semi-infinite domain in two dimensions. The expansion for the velocity potential is derived in terms of the corresponding eigenfunctions of the boundary-value problem. Utilizing such an expansion of the velocity potential, the symmetric wave source potentials or the so-called Green's function for the boundary-value problem of the flexural gravity wave maker is derived. Alternatively, utilizing the integral form of the wave source potential, the expansion formulae for the velocity potentials are recovered, which justifies the completeness of the eigenfunctions involved. As an application of the wave maker problem, oblique water wave scattering caused by cracks in a floating ice-sheet is analysed in the case of infinite depth.

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30

MANTZAVINOS, D., and A. S. FOKAS. "The unified transform for the heat equation: II. Non-separable boundary conditions in two dimensions." European Journal of Applied Mathematics 26, no. 6 (June 4, 2015): 887–916. http://dx.doi.org/10.1017/s0956792515000224.

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We use the two-dimensional heat equation as an illustrative example to show that the unified transform is capable of constructing analytical solutions for linear evolution partial differential equations (PDEs) in two spatial dimensions involving non-separable boundary conditions. Such non-separable boundary value problems apparently cannot be solved by the usual transforms. We note that the unified transform always yields integral expressions which, in contrast to the expressions obtained by the usual transforms, have the advantage that are uniformly convergent at the boundary. Thus, even for the cases of separable boundary value problems where the usual transforms can be implemented, the unified transform provides alternative solution expressions which have advantages for both numerical and asymptotic considerations. The former advantage is illustrated by providing the numerical evaluation of a typical boundary value problem, by extending the approach of Flyer and Fokas (2008Proc. R. Soc.464, 1823–1849). This work is the two-dimensional continuation of the heat equation with oblique Robin boundary conditions which was analysed in Mantzavinos and Fokas (2013Eur. J. Appl. Math.24(6), 857–886.

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31

Kim, Eun Heui. "Free boundary and mixed boundary value problems for quasilinear elliptic equations: tangential oblique derivative and degenerate Dirichlet boundary problems." Journal of Differential Equations 211, no. 2 (April 2005): 407–51. http://dx.doi.org/10.1016/j.jde.2004.07.024.

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32

吴, 婷婷. "The Gradient Estimation of Oblique Derivative Boundary Value Problems for Laplace Equation." Pure Mathematics 12, no. 11 (2022): 1851–58. http://dx.doi.org/10.12677/pm.2022.1211198.

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33

Emmrich, E. "Supraconvergence and Supercloseness of a Discretisation for Elliptic Third-kind Boundary-value Problems on Polygonal Domains." Computational Methods in Applied Mathematics 7, no. 2 (2007): 135–62. http://dx.doi.org/10.2478/cmam-2007-0008.

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AbstractThe third-kind boundary-value problem for a second-order elliptic equation on a polygonal domain with variable coefficients, mixed derivatives, and first-order terms is approximated by a linear finite element method with first-order accurate quadrature. The corresponding bilinear form does not need to be strongly positive. The discretisation is equivalent to a finite difference scheme. Although the discretisation is in general only first-order consistent, supraconvergence, i.e., convergence of higher order, is shown to take place even on nonuniform grids. If neither oblique boundary sections nor mixed derivatives occur, then the optimal order s is achieved. The supraconvergence result is equivalent to the supercloseness of the gradient.

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34

Gouidmi, Hamza, Abdelhadi Beghidja, Mohamadi Said, and Razik Benderradji. "Study of the Interaction of Shock Wave / Laminar Boundary Layer." Advanced Materials Research 274 (July 2011): 53–60. http://dx.doi.org/10.4028/www.scientific.net/amr.274.53.

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We are interested In this study to the interaction between oblique shock wave, induced by a surface of a supersonic nozzle with an angle of inclination of θw=8.5°, by a laminar boundary layer generated by a flat surface (reflection of oblique shock on a flat wall) . We studied also the problem of the development of the interaction zone and its unsteadiness. Our study is based on complex numerical simulation of interaction of shock wave / boundary layer and on their disturbance found within the interaction zone. This is the area of unsteady physical characteristics. This study was conducted under condition that the flow is compressible, of laminar and two-dimensional character. We treated also the point of detachment of the boundary layer by varying the value of the upstream Mach number. We compared our results (obtained by the commercial code FLUENT) with those found numerically and experimentally.

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35

Xu, Jinju, and Lu Xu. "Gradient estimates of mean curvature equations with semi-linear oblique boundary value problems." Proceedings of the American Mathematical Society 145, no. 8 (January 31, 2017): 3481–91. http://dx.doi.org/10.1090/proc/13483.

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36

Mehats, Florian, and Jean-Michel Roquejoffre. "A nonlinear oblique derivative boundary value problem for the heat equation Part 2: Singular self-similar solutions." Annales de l'Institut Henri Poincare (C) Non Linear Analysis 16, no. 6 (November 1999): 691–724. http://dx.doi.org/10.1016/s0294-1449(00)88184-6.

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37

Caffarelli, Luis A., and Jean-Michel Roquejoffre. "A nonlinear oblique derivative boundary value problem for the heat equation: Analogy with the porous medium equation." Annales de l'Institut Henri Poincare (C) Non Linear Analysis 19, no. 1 (2002): 41–80. http://dx.doi.org/10.1016/s0294-1449(01)00087-7.

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38

Medl’a, Matej, Karol Mikula, Róbert Čunderlík, and Marek Macák. "Numerical solution to the oblique derivative boundary value problem on non-uniform grids above the Earth topography." Journal of Geodesy 92, no. 1 (May 30, 2017): 1–19. http://dx.doi.org/10.1007/s00190-017-1040-z.

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39

Banasiak, J., and G. F. Roach. "On mixed boundary value problems of Dirichlet oblique-derivative type in plane domains with piecewise differentiable boundary." Journal of Differential Equations 79, no. 1 (May 1989): 111–31. http://dx.doi.org/10.1016/0022-0396(89)90116-2.

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40

Budzinskiy, S. S. "On the Zeros of Cross-Product Bessel Functions in Oblique Derivative Boundary-Value Problems." Moscow University Computational Mathematics and Cybernetics 44, no. 2 (April 2020): 53–60. http://dx.doi.org/10.3103/s0278641920020028.

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41

Borrelli, Alessandra, Giulia Giantesio, Maria Cristina Patria, Natalia C. Roşca, Alin V. Roşca, and Ioan Pop. "Influence of temperature and magnetic field on the oblique stagnation-point flow for a nanofluid past a vertical stretching/shrinking sheet." International Journal of Numerical Methods for Heat & Fluid Flow 28, no. 12 (December 3, 2018): 2874–94. http://dx.doi.org/10.1108/hff-12-2017-0497.

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Purpose This paper aims to consider the influence of the temperature and of an external magnetic field on the steady oblique stagnation-point flow for a Boussinesquian nanofluid past a stretching or shrinking sheet. Design/methodology/approach The flow is reduced through similarity transformations to an ordinary boundary value problem, which is solved numerically in MATLAB using the bvp4c function. The behavior of the solution is discussed physically, and some analytical considerations concerning existence of the solution and the occurrence of dual solutions are drawn. Findings The study of the influence of an external magnetic field on the oblique stagnation-point flow of a Buongiorno's Boussinesquian nanofluid is carried out. The fluid clashes on a vertical stretching or shrinking sheet. Dual solutions appear for suitable values of the parameters. Originality/value The present results are new and original.

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42

Osipov, Andrey V., and Thomas B. A. Senior. "Electromagnetic diffraction by arbitrary-angle impedance wedges." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 464, no. 2089 (October 23, 2007): 177–95. http://dx.doi.org/10.1098/rspa.2007.0163.

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The problem of the diffraction of a plane electromagnetic wave incident at an oblique angle on a wedge of arbitrary angle with general tensor impedance boundary conditions is solved using a semi-analytical approach. Application of Maliuzhinets' method transforms the boundary-value problem into coupled functional difference equations (FDEs) for two unknown Sommerfeld integral spectra in a basic strip. By explicitly separating out the singular parts of the spectra in the strip, followed by a partial inversion of the FDEs, we obtain integral representations of the regular parts of the spectra. The regular parts are then expanded in a Taylor series in terms of a new variable that conformally maps the strip on to a disc. This expansion reduces the integral representations to algebraic equations for the series coefficients and these are solved numerically. We examine the convergence of the procedure, compare the numerical solution with an available reference solution and present solutions of new problems.

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43

ČUNDERLÍK, Róbert, Matej MEDĽA, and Karol MIKULA. "Local quasigeoid modelling in Slovakia using the finite volume method on the discretized Earth's topography." Contributions to Geophysics and Geodesy 50, no. 3 (September 22, 2020): 287–302. http://dx.doi.org/10.31577/congeo.2020.50.3.1.

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The paper presents local quasigeoid modelling in Slovakia using the finite volume method (FVM). FVM is used to solve numerically the fixed gravimetric boundary value problem (FGBVP) on a 3D unstructured mesh created above the real Earth's surface. Terrestrial gravimetric measurements as input data represent the oblique derivative boundary conditions on the Earth's topography. To handle such oblique derivative problem, its tangential components are considered as surface advection terms regularized by a surface diffusion. The FVM numerical solution is fixed to the GOCE-based satellite-only geopotential model on the upper boundary at the altitude of 230 km. The horizontal resolution of the 3D computational domain is 0.002 × 0.002 deg and its discretization in the radial direction is changing with altitude. The created unstructured 3D mesh of finite volumes consists of 454,577,577 unknowns. The FVM numerical solution of FGBVP on such a detailed mesh leads to large-scale parallel computations requiring 245 GB of internal memory. It results in the disturbing potential obtained in the whole 3D computational domain. Its values on the discretized Earth's surface are transformed into the local quasigeoid model that is tested at 404 GNSS/levelling benchmarks. The standard deviation of residuals is 2.8 cm and decreases to 2.6 cm after removing 9 identified outliers. It indicates high accuracy of the obtained FVM-based local quasigeoid model in Slovakia.

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44

Giantesio, Giulia, Anna Verna, Natalia C. Roşca, Alin V. Rosca, and Ioan Pop. "MHD mixed convection oblique stagnation-point flow on a vertical plate." International Journal of Numerical Methods for Heat & Fluid Flow 27, no. 12 (December 4, 2017): 2744–67. http://dx.doi.org/10.1108/hff-12-2016-0486.

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Purpose This paper aims to study the problem of the steady plane oblique stagnation-point flow of an electrically conducting Newtonian fluid impinging on a heated vertical sheet. The temperature of the plate varies linearly with the distance from the stagnation point. Design/methodology/approach The governing boundary layer equations are transformed into a system of ordinary differential equations using the similarity transformations. The system is then solved numerically using the “bvp4c” function in MATLAB. Findings An exact similarity solution of the magnetohydrodynamic (MHD) Navier–Stokes equations under the Boussinesq approximation is obtained. Numerical solutions of the relevant functions and the structure of the flow field are presented and discussed for several values of the parameters which influence the motion: the Hartmann number, the parameter describing the oblique part of the motion, the Prandtl number (Pr) and the Richardson numbers. Dual solutions exist for several values of the parameters. Originality value The present results are original and new for the problem of MHD mixed convection oblique stagnation-point flow of a Newtonian fluid over a vertical flat plate, with the effect of induced magnetic field and temperature.

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45

Ermakov, V. G. "Homotopy classification of a certain set of multidimensional boundary-value problems of oblique derivative type." Russian Mathematical Surveys 43, no. 5 (October 31, 1988): 217–18. http://dx.doi.org/10.1070/rm1988v043n05abeh001940.

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46

Kawecki, Ellya L. "A Discontinuous Galerkin Finite Element Method fOR Uniformly Elliptic Two Dimensional Oblique Boundary-Value Problems." SIAM Journal on Numerical Analysis 57, no. 2 (January 2019): 751–78. http://dx.doi.org/10.1137/17m1155946.

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47

Trivedi, Kshma, Santanu Koley, and Kottala Panduranga. "Performance of an U-Shaped Oscillating Water Column Wave Energy Converter Device under Oblique Incident Waves." Fluids 6, no. 4 (April 1, 2021): 137. http://dx.doi.org/10.3390/fluids6040137.

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The present study deals with the performance of an U-shaped oscillating water column device under the action of oblique incident waves. To solve the associated boundary value problem, the dual boundary element method (DBEM) is used. Various physical parameters associated with the U-shaped OWC device, such as the radiation susceptance and conductance coefficients, and the hydrodynamic efficiency, are analyzed for a wide range of wave and structural parameters. The study reveals that the resonance in the efficiency curve occurs for smaller values of wavenumber with an increase in chamber length, submergence depth of the front wall and opening duct, and width of the opening duct. It is observed that with appropriate combinations of the angle of incidence and incident wavenumber, more than 90% efficiency in the U-shaped OWC device can be achieved.

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48

Ustilko, Ekaterina V., and Fiodar E. Lomovtsev. "Matching conditions for values of characteristic oblique derivative at the end of a string, initial data and right-hand side of the wave equation." Journal of the Belarusian State University. Mathematics and Informatics, no. 1 (March 29, 2020): 30–37. http://dx.doi.org/10.33581/2520-6508-2020-1-30-37.

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Sufficient matching conditions the time-dependent characteristic first derivatives in the boundary mode with the initial conditions and the more general vibration equation of a semi-bounded string are derived in the sets of solutions of all higher order smoothness orders. They generalize the previously found sufficient matching conditions in the case of a similar mixed problem for the simplest string vibration equation. The characteristic of non-stationary first oblique derivatives in the boundary mode means that at each moment of time they are directed along the critical characteristic.

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49

Lieberman, Gary A. "On The Hölder Gradient Estimate For Solutions Of Nonlinear Elliptic And Parabolic Oblique Boundary Value Problems." Communications in Partial Differential Equations 15, no. 4 (January 1990): 515–23. http://dx.doi.org/10.1080/03605309908820696.

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50

Costabel, Martin, and Monique Dauge. "General edge asymptotics of solutions of second-order elliptic boundary value problems I." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 123, no. 1 (1993): 109–55. http://dx.doi.org/10.1017/s0308210500021272.

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SynopsisThis is the first of two papers in which we study the singularities of solutions of second-order linear elliptic boundary value problems at the edges of piecewise analytic domains in ℝ3. When the opening angle at the edge is variable, there appears the phenomenon of “crossing” of the exponents of singularities. For this case, we introduce the appropriate combinations of the simple tensor product singularities that allow us to give estimates in ordinary and weighted Sobolev spaces for the regular part of the solution and for the coefficients of the singularities. These combinations appear in a natural way as sections of an analytic bundle above the edge. Their behaviour is described with the help of divided differences of powers of the distance to the edge. The class of operators considered includes second-order elliptic operators with analytic complex-valued coefficients with mixed Dirichlet, Neumann or oblique derivative conditions. With our description of the singularities we are able to remove some restrictive hypotheses that were previously made in other works. In this first part, we prove the basic facts in a simplified framework. Nevertheless the tools we use are essentially the same in the general situation.

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