On a nonlocal problem for parabolic equation with time dependent coefficients

Advances in Difference Equations

Le Dinh Long¹  Ho Duy Binh¹  Nguyen Duc Phuong²  Dang Van Yen³ 

[1] Division of Applied Mathematics, Thu Dau Mot University, Binh Duong Province, Vietnam;Faculty of Fundamental Science, Industrial University of Ho Chi Minh City, Ho Chi Minh City, Vietnam;Faculty of Information Technology, Ho Chi Minh City University of Technology, Ho Chi Minh City, Vietnam;

关键词: Parabolic equation;    Existence and regularity;    Conformable derivative;    35R11;    35B65;    26A33;   

DOI  :  10.1186/s13662-021-03370-4

来源: Springer

【 摘 要 】

This paper is devoted to the study of existence and uniqueness of a mild solution for a parabolic equation with conformable derivative. The nonlocal problem for parabolic equations appears in many various applications, such as physics, biology. The first part of this paper is to consider the well-posedness and regularity of the mild solution. The second one is to investigate the existence by using Banach fixed point theory.

【 授权许可】

CC BY