A variant of quasi‐reversibility method for a class of heat equations with involution perturbation

Abstract

The paper is devoted to investigating a Cauchy problem governed by nonclassical heat equation with involution. The problem is severely ill‐posed in the sense of Hadamard by violating the continuous dependence upon the input Cauchy data. Therefore, in order to obtain a stable solution, we shall use a modified Pseudo‐Parabolic Regularization Method. The main idea is to add a correction term by introducing a third‐order derivation operator to formulate a sequence of well‐posed problems that depend on a regularization parameter ε . Further, we show that the approximate problems are well posed, and we prove some convergence results.

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