On a Kirchhoff diffusion equation with integral condition

Advances in Difference Equations

Nguyen Huu Can¹  Dumitru Baleanu²  Danh Hua Quoc Nam³  Nguyen Hoang Luc⁴ 

[1] Applied Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam;Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, 06530, Ankara, Turkey;Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan;Institute of Space Sciences, P.O. Box, MG-23, R 76900, Magurele-Bucharest, Romania;Division of Applied Mathematics, Thu Dau Mot University, Binh Duong Province, Vietnam;Institute of Research and Development, Duy Tan University, Da Nang, Vietnam;

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

DOI  :  10.1186/s13662-020-03077-y

来源: Springer

【 摘 要 】

This paper is devoted to Kirchhoff-type parabolic problem with nonlocal integral condition. Our problem has many applications in modeling physical and biological phenomena. The first part of our paper concerns the local existence of the mild solution in Hilbert scales. Our results can be studied into two cases: homogeneous case and inhomogeneous case. In order to overcome difficulties, we applied Banach fixed point theorem and some new techniques on Sobolev spaces. The second part of the paper is to derive the ill-posedness of the mild solution in the sense of Hadamard.

【 授权许可】

CC BY