Existence of solutions for impulsive parabolic partial differential equations

Abdelkader Boucherif; Ali S. Al-Qahtani; Bilal Chanane

doi:10.1080/01630563.2015.1031381

Existence of solutions for impulsive parabolic partial differential equations

Abdelkader Boucherif^*
, Ali S. Al-Qahtani
, Bilal Chanane

^*Corresponding author for this work

King Fahd University of Petroleum & Minerals

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	730-747
Number of pages	18
Journal	Numerical Functional Analysis and Optimization
Volume	36
Issue number	6
DOIs	https://doi.org/10.1080/01630563.2015.1031381
State	Published - 3 Jun 2015

Bibliographical note

Publisher Copyright:
Copyright © 2015 Taylor & Francis Group, LLC.

Keywords

Fixed point theorems
Green's function
Impulse effects
Integral representation of solutions
Parabolic partial differential equations

ASJC Scopus subject areas

Analysis
Signal Processing
Computer Science Applications
Control and Optimization

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10.1080/01630563.2015.1031381

Cite this

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abstract = "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.",

keywords = "Fixed point theorems, Green's function, Impulse effects, Integral representation of solutions, Parabolic partial differential equations",

author = "Abdelkader Boucherif and Al-Qahtani, \{Ali S.\} and Bilal Chanane",

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AU - Boucherif, Abdelkader

AU - Al-Qahtani, Ali S.

AU - Chanane, Bilal

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Y1 - 2015/6/3

N2 - 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.

AB - 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.

KW - Fixed point theorems

KW - Green's function

KW - Impulse effects

KW - Integral representation of solutions

KW - Parabolic partial differential equations

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JF - Numerical Functional Analysis and Optimization

IS - 6

ER -

Existence of solutions for impulsive parabolic partial differential equations

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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