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Abdelkader Boucherif Ali S. Al-Qahtani Bilal Chanane 《Numerical Functional Analysis & Optimization》2013,34(6):730-747
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. 相似文献