Well-posed results for nonlocal biparabolic equation with linear and nonlinear source terms

Advances in Difference Equations

Van Thinh Nguyen¹  Le Dinh Long²  Kim Van Ho Thi²  Ho Duy Binh² 

[1] Department of Civil and Environmental Engineering, Seoul National University, Seoul, South Korea;Division of Applied Mathematics, Thu Dau Mot University, Thu Dau Mot, Binh Duong Province, Vietnam;

关键词: Biparabolic equation;    Source term;    Nonlocal condition;    Mild solution;    Existence;    Uniqueness;    Convergence;   

DOI  :  10.1186/s13662-021-03602-7

来源: Springer

【 摘 要 】

In this paper, we consider the biparabolic problem under nonlocal conditions with both linear and nonlinear source terms. We derive the regularity property of the mild solution for the linear source term while we apply the Banach fixed-point theorem to study the existence and uniqueness of the mild solution for the nonlinear source term. In both cases, we show that the mild solution of our problem converges to the solution of an initial value problem as the parameter epsilon tends to zero. The novelty in our study can be considered as one of the first results on biparabolic equations with nonlocal conditions.

【 授权许可】

CC BY