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

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