Abstract Volterra integrodifferential equations with applications to parabolic models with memory

被引：32

作者：

de Andrade, Bruno ^{[2
]}

Viana, Arlucio ^{[1
]}

机构：

[1] Univ Fed Sergipe, Dept Matemat, Ave Vereador Olimpio Grande, Itabaiana, SE, Brazil

[2] Univ Fed Sergipe, Dept Matemat, Ave Rosa Else, Sao Cristovao, SE, Brazil

来源：

MATHEMATISCHE ANNALEN | 2017年 / 369卷 / 3-4期

关键词：

FUJITA CRITICAL EXPONENT; NONLINEAR HEAT-EQUATION; NAVIER-STOKES EQUATION; ASYMPTOTIC STABILITY; GLOBAL-SOLUTIONS; WELL-POSEDNESS; WAVE-EQUATION; BEHAVIOR; SYSTEMS; NONEXISTENCE;

D O I：

10.1007/s00208-016-1469-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we are concerned with local existence, regularity and continuous dependence upon the initial data of -regular mild solutions for the abstract integrodifferential equation (1, 2). We also present a result on unique continuation and a blow-up alternative for an -regular mild solution of (1, 2). Finally, we apply our results to three interesting models: Navier-Stokes equations with memory, diffusion equations with memory and a strongly damped plate equation with memory.

引用

页码：1131 / 1175

页数：45

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