Existence of solutions for a class of heat equations involving the mean curvature operator

被引：2

作者：

Alves, Claudianor O. O. ^{[1
]}

Boudjeriou, Tahir ^{[2
]}

机构：

[1] Univ Fed Campina Grande, Unidade Academ Matemat, BR-58429970 Campina Grande, PB, Brazil

[2] Univ Boumerdes, Inst Elect & Elect Engn, Dept Basic Teaching, Boumerdes 35000, Algeria

来源：

ANALYSIS AND MATHEMATICAL PHYSICS | 2023年 / 13卷 / 01期

关键词：

EVOLUTIONARY SURFACES; PARABOLIC EQUATION; DIRICHLET; SPACE;

D O I：

10.1007/s13324-022-00774-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The goal of this paper is to show the existence of a bounded variation solution, which is based on the Anzellotti pairing to an evolution problem associated with the mini-mal surface equations. A key ingredient in the proof is to approximate the parabolic minimal surface problem by a quasilinear parabolic problem involving a parameter p > 1, and then by establishing some energy estimates independent of p, we take the limit as p -> 1(+) to obtain the desired result.

引用

页数：27

共 50 条

[1] Existence of solutions for a class of heat equations involving the mean curvature operator
Claudianor O. Alves
Tahir Boudjeriou
Analysis and Mathematical Physics, 2023, 13
[2] Existence of Solutions for the Discrete Dirichlet Problem Involving p-Mean Curvature Operator
Wang, Jianxia
Zhou, Zhan
DISCRETE DYNAMICS IN NATURE AND SOCIETY, 2020, 2020
[3] Existence of solutions for a class of operator equations
Feng, Xiaojing
FIXED POINT THEORY AND APPLICATIONS, 2015,
[4] Existence of solutions for a class of operator equations
Xiaojing Feng
Fixed Point Theory and Applications, 2015
[5] On unbounded solutions for differential equations with mean curvature operator
Dosla, Zuzana
Marini, Mauro
Matucci, Serena
CZECHOSLOVAK MATHEMATICAL JOURNAL, 2025, 75 (01) : 215 - 234
[6] EXISTENCE AND UNIQUENESS OF SOLUTIONS TO A CLASS OF OPERATOR EQUATIONS
李寿佛
Chinese Science Bulletin, 1992, (19) : 1585 - 1589
[7] On the existence of large solutions for equations of prescribed mean curvature
Dipartimento di Matematica, Cagliari, Italy
Nonlinear Anal Theory Methods Appl, 4 (571-583):
[8] On the existence of large solutions for equations of prescribed mean curvature
Greco, A
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1998, 34 (04) : 571 - 583
[9] Heteroclinic solutions for a difference equation involving the mean curvature operator
Wang, Shaohong
Zhou, Zhan
APPLIED MATHEMATICS LETTERS, 2024, 147
[10] Existence and stability of solutions of a class of hybrid fractional differential equations involving RL-operator
Ferraoun, Soumia
Dahmani, Zoubir
JOURNAL OF INTERDISCIPLINARY MATHEMATICS, 2020, 23 (04) : 885 - 903

← 1 2 3 4 5 →