Global and blowup solutions of a mixed problem with nonlinear boundary conditions for a one-dimensional semilinear wave equation

被引：4

作者：

Kharibegashvili, S. S. ^{[1
,2
]}

Jokhadze, O. M. ^{[1
,3
]}

机构：

[1] Georgian Acad Sci, Razmadze Math Inst, GE-380060 Tbilisi, Georgia

[2] Georgian Tech Univ, Tbilisi, Georgia

[3] Tbilisi State Univ, Tbilisi, Georgia

来源：

SBORNIK MATHEMATICS | 2014年 / 205卷 / 04期

关键词：

semilinear wave equation; nonlinear boundary conditions; a priori estimate; comparison theorems; global and blowup solutions; NONEXISTENCE; EXISTENCE; STABILITY;

D O I：

10.1070/SM2014v205n04ABEH004388

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A mixed problem for a one-dimensional semilinear wave equation with nonlinear boundary conditions is considered. Conditions of this type occur, for example, in the description of the longitudinal oscillations of a spring fastened elastically at one end, but not in accordance with Hooke's linear law. Uniqueness and existence questions are investigated for global and blowup solutions to this problem, in particular how they depend on the nature of the nonlinearities involved in the equation and the boundary conditions.

引用

页码：573 / 599

页数：27

共 50 条

[41] Integral means of solutions of the one-dimensional Poisson equation with Robin boundary conditions
Papadimitriou, Christos
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2025, 541 (02)
[42] ON SOLUTION EXISTENCE THEOREM IN THE MIXED PROBLEM FOR ONE-DIMENSIONAL WAVE-EQUATION
CHERNYATIN, VA
VESTNIK MOSKOVSKOGO UNIVERSITETA SERIYA 1 MATEMATIKA MEKHANIKA, 1987, (06): : 9 - 21
[43] Existence of smooth solutions to a one-dimensional nonlinear degenerate variational wave equation
Hu, Yanbo
Wang, Guodong
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2017, 165 : 80 - 101
[44] Global existence of solutions to a one-dimensional free boundary problem of hyperbolic type
Nakane, K
PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 2001, 77 (07) : 103 - 107
[45] VARIATIONAL APPROACH TO STABILITY OF SEMILINEAR WAVE EQUATION WITH NONLINEAR BOUNDARY CONDITIONS
Nowakowski, Andrezej
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2014, 19 (08): : 2603 - 2616
[46] POSITIVE SOLUTIONS FOR THE ONE-DIMENSIONAL p-LAPLACIAN WITH NONLINEAR BOUNDARY CONDITIONS
Hai, D. D.
Wang, X.
OPUSCULA MATHEMATICA, 2019, 39 (05) : 675 - 689
[47] On global solutions for quasilinear one-dimensional parabolic problems with dynamical boundary conditions
Gvelesiani, Simon
Lippoth, Friedrich
Walker, Christoph
JOURNAL OF DIFFERENTIAL EQUATIONS, 2015, 259 (12) : 7060 - 7085
[48] Time-periodic solutions to the one-dimensional wave equation with periodic or anti-periodic boundary conditions
Ji, Shuguan
Li, Yong
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2007, 137 : 349 - 371
[49] Blowup rate of solutions for a semilinear heat equation with the Neumann boundary condition
Mizoguchi, N
JOURNAL OF DIFFERENTIAL EQUATIONS, 2003, 193 (01) : 212 - 238
[50] MIXED PROBLEM WITH DISCONTINUOUS BOUNDARY CONDITIONS FOR WAVE EQUATION
CHEKHLOV, VI
DOKLADY AKADEMII NAUK SSSR, 1968, 183 (04): : 787 - &

← 1 2 3 4 5 →