Approximation of elliptic and parabolic equations with Dirichlet boundary conditions

Youchan Kim; Seungjin Ryu; Pilsoo Shin

doi:10.3934/mine.2023079

Approximation of elliptic and parabolic equations with Dirichlet boundary conditions

Youchan Kim
, Seungjin Ryu
, Pilsoo Shin

Department of Mathematics

Kyonggi University

Research output: Contribution to journal › Article › peer-review

Abstract

We obtain an approximation result of the weak solutions to elliptic and parabolic equations with Dirichlet boundary conditions. We show that the weak solution can be obtained with a limit of approximations by regularizing the nonlinearities and approximating the domains.

Original language	English
Journal	Mathematics In Engineering
Volume	5
Issue number	4
DOIs	https://doi.org/10.3934/mine.2023079
State	Published - 2023

Keywords

approximations
nonlinear elliptic equations
nonlinear parabolic equations

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10.3934/mine.2023079

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title = "Approximation of elliptic and parabolic equations with Dirichlet boundary conditions",

abstract = "We obtain an approximation result of the weak solutions to elliptic and parabolic equations with Dirichlet boundary conditions. We show that the weak solution can be obtained with a limit of approximations by regularizing the nonlinearities and approximating the domains.",

keywords = "approximations, nonlinear elliptic equations, nonlinear parabolic equations",

author = "Youchan Kim and Seungjin Ryu and Pilsoo Shin",

note = "Publisher Copyright: {\textcopyright} 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)",

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AU - Kim, Youchan

AU - Ryu, Seungjin

AU - Shin, Pilsoo

N1 - Publisher Copyright: © 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)

PY - 2023

Y1 - 2023

N2 - We obtain an approximation result of the weak solutions to elliptic and parabolic equations with Dirichlet boundary conditions. We show that the weak solution can be obtained with a limit of approximations by regularizing the nonlinearities and approximating the domains.

AB - We obtain an approximation result of the weak solutions to elliptic and parabolic equations with Dirichlet boundary conditions. We show that the weak solution can be obtained with a limit of approximations by regularizing the nonlinearities and approximating the domains.

KW - approximations

KW - nonlinear elliptic equations

KW - nonlinear parabolic equations

UR - https://www.scopus.com/pages/publications/85154584561

U2 - 10.3934/mine.2023079

DO - 10.3934/mine.2023079

M3 - Article

AN - SCOPUS:85154584561

SN - 2640-3501

VL - 5

JO - Mathematics In Engineering

JF - Mathematics In Engineering

IS - 4

ER -

Approximation of elliptic and parabolic equations with Dirichlet boundary conditions

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