Existence and non-existence of global solutions to initial boundary value problems for nonlinear evolution equations with strong dissipation

被引：1

作者：

Kubo, Akisato ^{[1
]}

Loheac, Jean-Pierre ^{[2
,3
]}

机构：

[1] Fujita Hlth Univ, Sch Hlth Sci, Dept Math, Aichi 4701192, Japan

[2] Univ Lyon, Ecole Cent Lyon, CNRS, Inst Camille Jordan,Dept Math Informat,UMR 5208, F-69134 Ecully, France

[3] Independent Moscow Univ, Lab JV Poncelet, CNRS, UMI 2615, Moscow 119002, Russia

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2009年 / 71卷 / 12期

基金：

日本学术振兴会;

关键词：

Evolution equation; Strong dissipation; Blow-up; Global existence; STABILITY; UNIQUENESS;

D O I：

10.1016/j.na.2009.06.053

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The main purpose in this paper is to investigate existence and non-existence of global solutions of the initial Dirichlet boundary value problem for evolution equations with strong dissipation. Many authors studied classes consisting of such types of equations for which initial boundary value problems possess global solutions. For this purpose we consider a related problem and seek global solutions and blow-up solutions of it depending on whether it belongs to such classes or not. (C) 2009 Elsevier Ltd. All rights reserved.

引用

页码：E2797 / E2806

页数：10

共 50 条

[21] Local and global existence of solutions to initial value problems of nonlinear Kaup-Kupershmidt equations
Tao, SP
Cui, SB
ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2005, 21 (04) : 881 - 892
[22] A numerical proof algorithm for the non-existence of solutions to elliptic boundary value problems
Sekine, Kouta
Nakao, Mitsuhiro T.
Oishi, Shin'ichi
Kashiwagi, Masahide
APPLIED NUMERICAL MATHEMATICS, 2021, 169 : 87 - 107
[23] Existence and non-existence results for elliptic exterior problems with nonlinear boundary conditions
Ionica, Andrei
ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA, 2009, 17 (01): : 105 - 118
[24] Existence and non-existence of global solutions for a class of non-linear wave equations
Chen, GW
Yang, ZJ
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2000, 23 (07) : 615 - 631
[25] EXISTENCE OF CLASSICAL SOLUTIONS FOR INITIAL BOUNDARY VALUE PROBLEMS FOR NONLINEAR DISPERSIVE EQUATIONS OF ODD-ORDERS
Georgiev, Svetlin Georgiev
Kheloufi, Arezki
Mebarki, Karima
METHODS OF FUNCTIONAL ANALYSIS AND TOPOLOGY, 2022, 28 (03): : 228 - 241
[26] Existence and uniqueness of solutions of initial value problems for nonlinear fractional differential equations
Deng, Jiqin
Ma, Lifeng
APPLIED MATHEMATICS LETTERS, 2010, 23 (06) : 676 - 680
[27] Existence and non-existence results for quasilinear elliptic exterior problems with nonlinear boundary conditions
Filippucci, Roberta
Pucci, Patrizia
Radulescu, Vicentiu
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2008, 33 (04) : 706 - 717
[28] Existence and uniqueness of mild solutions to initial value problems for fractional evolution equations
Sin, Chung-Sik
In, Hyok-Chol
Kim, Kwang-Chol
ADVANCES IN DIFFERENCE EQUATIONS, 2018,
[29] Existence of solutions for irregular boundary value problems of nonlinear fractional differential equations
Ahmad, Bashir
APPLIED MATHEMATICS LETTERS, 2010, 23 (04) : 390 - 394
[30] On The Existence of Positive Solutions for Boundary Value Problems of Nonlinear Fractional Differential Equations
Zhao, Yige
Sun, Shurong
PROCEEDINGS OF THE 7TH CONFERENCE ON BIOLOGICAL DYNAMIC SYSTEM AND STABILITY OF DIFFERENTIAL EQUATION, VOLS I AND II, 2010, : 682 - 685

← 1 2 3 4 5 →