EXISTENCE AND UNIQUENESS RESULT OF A SOLUTION WITH NUMERIC SIMULATION FOR NONLOCAL THERMISTOR PROBLEM WITH THE PRESENCE OF MEMORY TERM
摘要
A thermistor is a ceramic electrical circuit component with temperature-dependent electric conductivity. The mathematical description of this device is based on the nonlinear parabolic equation describing the temperature. In this work, we investigate the model in which the right-hand side of the equation representing temperature evolution contains a nonlocal term. To show the existence and uniqueness of a solution, we specifically employ the Faedo–Galerkin method and the compactness technique. We also present a numerical example to illustrate the evolution of the solution and validate the proposed approach given in Eq.