Premium
A variant of quasi‐reversibility method for a class of heat equations with involution perturbation
Author(s) -
Roumaissa Sassane,
Nadjib Boussetila,
Faouzia Rebbani
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6780
Subject(s) - mathematics , hadamard transform , well posed problem , regularization (linguistics) , heat equation , cauchy problem , perturbation (astronomy) , involution (esoterism) , cauchy distribution , cauchy's convergence test , initial value problem , mathematical analysis , parabolic partial differential equation , backus–gilbert method , inverse problem , regularization perspectives on support vector machines , cauchy boundary condition , partial differential equation , boundary value problem , tikhonov regularization , computer science , physics , quantum mechanics , artificial intelligence , politics , political science , law , free boundary problem
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.