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

• Main Authors: Le Dinh Long, Ho Duy Binh, Kim Van Ho Thi, Van Thinh Nguyen
• Format: Article
• Language: English
• Published: SpringerOpen 2021-10-01
• Series: Advances in Difference Equations
• Subjects: Biparabolic equation; Source term; Nonlocal condition; Mild solution; Existence; Uniqueness
• Online Access: https://doi.org/10.1186/s13662-021-03602-7

Abstract 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.