Existence of Solutions for Impulsive Parabolic Partial Differential Equations

被引：4

作者：

Boucherif, Abdelkader ^{[1
]}

Al-Qahtani, Ali S. ^{[2
]}

Chanane, Bilal ^{[1
]}

机构：

[1] King Fahd Univ Petr & Minerals, Dept Math & Stat, Dhahran 31261, Saudi Arabia

[2] King Khalid Univ, Dept Math, Abha, Saudi Arabia

来源：

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION | 2015年 / 36卷 / 06期

关键词：

Integral representation of solutions; Green's function; Impulse effects; Fixed point theorems; Parabolic partial differential equations; 35R12; 35K20; 35C15; HEAT-EQUATIONS;

D O I：

10.1080/01630563.2015.1031381

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We discuss the propagation of heat along a homogeneous rod of length A under the influence of a nonlinear heat source and impulsive effects at fixed times. This problem is described by an initial-boundary value problem for a nonlinear parabolic partial differential equation subjected to impulsive effects at fixed times. Using Green's function, we convert the problem into a nonlinear integral equation. Sufficient conditions are provided that enable the application of fixed point theorems to prove existence and uniqueness of solutions.

引用

页码：730 / 747

页数：18

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