Global and blow-up solutions for a nonlinear reaction diffusion equation with Robin boundary conditions

• Published in: Boundary value problems Vol. 2020; no. 1; pp. 1 - 19
• Main Authors: Tian, Huimin, Zhang, Lingling
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 31.03.2020; Hindawi Limited; SpringerOpen
• Subjects: Analysis; Approximations and Expansions; Blow-up; Boundary conditions; Difference and Functional Equations; Global; Lower and upper bounds; Lower bounds; Mathematics; Mathematics and Statistics; Nonlinear equations; Ordinary Differential Equations; Partial Differential Equations; Reaction diffusion equations; Upper bounds; Reaction diffusion equations; Lower and upper bounds; Global; Blow-up
• ISSN: 1687-2770; 1687-2762; 1687-2770
• DOI: 10.1186/s13661-020-01363-y

In the paper, we investigate global and blow-up solutions for a class of nonlinear reaction diffusion equations with Robin boundary conditions. By using auxiliary functions and a first-order differential inequality technique, we establish conditions on the data to prove the existence of global solution. Moreover, based on maximum principles, we obtain a criterion that guarantees the occurrence of the blow-up. When blow-up occurs, we discuss an upper bound and a lower bound on blow-up time. At last, we apply two examples to illustrate our main results.