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Existence of Solutions for Impulsive Parabolic Partial Differential Equations |
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| Authors: | Abdelkader Boucherif Ali S Al-Qahtani Bilal Chanane |
| Institution: | 1. Department of Mathematics and Statistics , King Fahd University of Petroleum and Minerals , Dhahran , Saudi Arabia aboucher@kfupm.edu.sa;3. Department of Mathematics , King Khalid University , Abha , Saudi Arabia;4. Department of Mathematics and Statistics , King Fahd University of Petroleum and Minerals , Dhahran , Saudi Arabia |
| 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 |