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Relevant bibliographies by topics / Nonlinear parabolic and elliptic boundary values problems

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Journal articles

Academic literature on the topic 'Nonlinear parabolic and elliptic boundary values problems'

Author: Grafiati

Published: 10 March 2023

Last updated: 11 March 2023

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Journal articles on the topic "Nonlinear parabolic and elliptic boundary values problems"

1

Hamamuki, Nao, and Qing Liu. "A deterministic game interpretation for fully nonlinear parabolic equations with dynamic boundary conditions." ESAIM: Control, Optimisation and Calculus of Variations 26 (2020): 13. http://dx.doi.org/10.1051/cocv/2019076.

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This paper is devoted to deterministic discrete game-theoretic interpretations for fully nonlinear parabolic and elliptic equations with nonlinear dynamic boundary conditions. It is known that the classical Neumann boundary condition for general parabolic or elliptic equations can be generated by including reflections on the boundary to the interior optimal control or game interpretations. We study a dynamic version of such type of boundary problems, generalizing the discrete game-theoretic approach proposed by Kohn-Serfaty (2006, 2010) for Cauchy problems and later developed by Giga-Liu (2009) and Daniel (2013) for Neumann type boundary problems.

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2

Shangbin, Cui. "Some comparison and uniqueness theorems for nonlinear elliptic boundary value problems and nonlinear parabolic initial-boundary value problems." Nonlinear Analysis: Theory, Methods & Applications 29, no. 9 (1997): 1079–90. http://dx.doi.org/10.1016/s0362-546x(96)00097-1.

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3

Chow, S. S., and R. D. Lazarov. "Superconvergence analysis of flux computations for nonlinear problems." Bulletin of the Australian Mathematical Society 40, no. 3 (1989): 465–79. http://dx.doi.org/10.1017/s0004972700017536.

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In this paper we consider the error estimates for some boundary-flux calculation procedures applied to two-point semilinear and strongly nonlinear elliptic boundary value problems. The case of semilinear parabolic problems is also studied. We prove that the computed flux is superconvergent with second and third order of convergence for linear and quadratic elements respectively. Corresponding estimates for higher order elements may also be obtained by following the general line of argument.

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4

SHAKHMUROV, VELI B., and AIDA SAHMUROVA. "Mixed problems for degenerate abstract parabolic equations and applications." Carpathian Journal of Mathematics 34, no. 2 (2018): 247–54. http://dx.doi.org/10.37193/cjm.2018.02.13.

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Degenerate abstract parabolic equations with variable coefficients are studied. Here the boundary conditions are nonlocal. The maximal regularity properties of solutions for elliptic and parabolic problems and Strichartz type estimates in mixed Lebesgue spaces are obtained. Moreover, the existence and uniqueness of optimal regular solution of mixed problem for nonlinear parabolic equation is established. Note that, these problems arise in fluid mechanics and environmental engineering.

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5

Gavrilyuk, I. P. "Approximation of the Operator Exponential and Applications." Computational Methods in Applied Mathematics 7, no. 4 (2007): 294–320. http://dx.doi.org/10.2478/cmam-2007-0019.

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AbstractA review of the exponentially convergent approximations to the operator exponential is given. The applications to inhomogeneous parabolic and elliptic equations, nonlinear parabolic equations, tensor-product approximations of multidimensional solution operators as well as to parabolic problems with time dependent coefficients and boundary conditions are discussed.

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6

Indrei, Emanuel, and Andreas Minne. "Regularity of solutions to fully nonlinear elliptic and parabolic free boundary problems." Annales de l'Institut Henri Poincare (C) Non Linear Analysis 33, no. 5 (2016): 1259–77. http://dx.doi.org/10.1016/j.anihpc.2015.03.009.

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7

I. Vishik, Mark, and Sergey Zelik. "Attractors for the nonlinear elliptic boundary value problems and their parabolic singular limit." Communications on Pure & Applied Analysis 13, no. 5 (2014): 2059–93. http://dx.doi.org/10.3934/cpaa.2014.13.2059.

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8

Zhang, Qi S. "A general blow-up result on nonlinear boundary-value problems on exterior domains." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 131, no. 2 (2001): 451–75. http://dx.doi.org/10.1017/s0308210500000950.

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In the first part, we study several exterior boundary-value problems covering three types of semilinear equations: elliptic, parabolic and hyperbolic. By a unified approach, we show that these problems share a common critical behaviour. In the second part we prove a blow-up result for an inhomogeneous porous medium equation with the critical exponent, which was left open in a previous paper.

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9

Andreu, F., N. Igbida, J. M. Mazón, and J. Toledo. "Renormalized solutions for degenerate elliptic–parabolic problems with nonlinear dynamical boundary conditions and L1-data." Journal of Differential Equations 244, no. 11 (2008): 2764–803. http://dx.doi.org/10.1016/j.jde.2008.02.022.

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10

Galkowski, Jeffrey. "Pseudospectra of semiclassical boundary value problems." Journal of the Institute of Mathematics of Jussieu 14, no. 2 (2014): 405–49. http://dx.doi.org/10.1017/s1474748014000061.

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AbstractWe consider operators$ - \Delta + X $, where$ X $is a constant vector field, in a bounded domain, and show spectral instability when the domain is expanded by scaling. More generally, we consider semiclassical elliptic boundary value problems which exhibit spectral instability for small values of the semiclassical parameter$h$, which should be thought of as the reciprocal of the Péclet constant. This instability is due to the presence of the boundary: just as in the case of$ - \Delta + X $, some of our operators are normal when considered on$\mathbb{R}^d$. We characterize the semiclassical pseudospectrum of such problems as well as the areas of concentration of quasimodes. As an application, we prove a result about exit times for diffusion processes in bounded domains. We also demonstrate instability for a class of spectrally stable nonlinear evolution problems that are associated with these elliptic operators.

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