Estimates for the lifespan of solutions of an initial-boundary value problem for a nonlinear Sobolev equation with variable coefficient

被引：4

作者：

Aristov, A. I.

机构：

来源：

DIFFERENTIAL EQUATIONS | 2012年 / 48卷 / 06期

关键词：

Positive Root; Quadrature Formula; Sobolev Type; Sobolev Equation; Chastnykh Proizvodnykh;

D O I：

10.1134/S0012266112060031

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider an initial-boundary value problem for a nonlinear equation of Sobolev type with variable coefficient multiplying the power-law nonlinearity. We obtain sufficient conditions for both time-global and time-local solvability. In the case of local (but not global) solvability, we find two-sided estimates for the lifespan of the solution in the form of quadrature formulas and indicate special cases in which a closed form of these estimates is possible.

引用

页码：787 / 795

页数：9