On initial inverse problem for nonlinear couple heat with Kirchhoff type

Advances in Difference Equations

Danh Hua Quoc Nam¹ 

[1] Department of Mathematics and Computer Science, University of Science, Ho Chi Minh City, Vietnam;Vietnam National University, Ho Chi Minh City, Vietnam;Division of Applied Mathematics, Thu Dau Mot University, Binh Duong Province, Vietnam;

关键词: Kirchhoff-type problems;    Nonlocal problem;    Well-posedness;    Regularization;    35R11;    35B65;    26A33;   

DOI  :  10.1186/s13662-021-03655-8

来源: Springer

【 摘 要 】

The main objective of the paper is to study the final model for the Kirchhoff-type parabolic system. Such type problems have many applications in physical and biological phenomena. Under some smoothness of the final Cauchy data, we prove that the problem has a unique mild solution. The main tool is Banach’s fixed point theorem. We also consider the non-well-posed problem in the Hadamard sense. Finally, we apply truncation method to regularize our problem. The paper is motivated by the work of Tuan, Nam, and Nhat [Comput. Math. Appl. 77(1):15–33, 2019].

【 授权许可】

CC BY