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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
