ESTIMATES FOR MILD SOLUTIONS TO SEMILINEAR CAUCHY PROBLEMS

被引：0

作者：

Burazin, Kresimir ^{[1
]}

Erceg, Marko ^{[2
]}

机构：

[1] Univ Osijek, Dept Math, Osijek, Croatia

[2] Univ Zagreb, Fac Sci, Dept Math, Zagreb 41000, Croatia

来源：

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS | 2014年

关键词：

Semigroup; abstract Cauchy problem; blow-up; quenching time;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The existence (and uniqueness) results on mild solutions of the abstract semilinear Cauchy problems in Banach spaces are well known. Following the results of Tartar (2008) and Burazin (2008) in the case of decoupled hyperbolic systems, we give an alternative proof, which enables us to derive an estimate on the mild solution and its time of existence. The nonlinear term in the equation is allowed to be time-dependent. We discuss the optimality of the derived estimate by testing it on three examples: the linear heat equation, the semilinear heat equation that models dynamic deflection of an elastic membrane, and the semilinear Schrodinger equation with time-dependent non-linearity, that appear in the modelling of numerous physical phenomena.

引用

页数：10

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