Abstract
This paper deals with the global existence and blow-up of the solution for a class of nonlinear reaction diffusion problems. The purpose of this paper is to establish conditions on the data to guarantee the blow-up of the solution at some finite time, and conditions to ensure that the solution remains global. In addition, an upper bound for the ‘blow-up time’, an upper estimate of the ‘blow-up rate’, and an upper estimate of the global solution are also specified. Finally, as applications of the obtained results, some examples are presented.
Highlights
1 Introduction The global existence and blow-up for nonlinear reaction diffusion equations have been widely studied in recent years
The necessary and sufficient conditions characterized by functions a and f were given for the global existence and blow-up solution
By constructing completely different auxiliary functions from those in [, ] and technically using maximum principles, we obtain the conditions on the data to guarantee the blow-up of the solution at some finite time, and conditions to ensure that the solution remains global
Summary
The global existence and blow-up for nonlinear reaction diffusion equations have been widely studied in recent years (see, for instance, [ – ]). Many authors discussed the global existence and blow-up for nonlinear reaction diffusion equations with Neumann boundary conditions and obtained a lot of interesting results [ – ]. The necessary and sufficient conditions characterized by functions a and f were given for the global existence and blow-up solution. The sufficient conditions were obtained there for the existence of global and blow-up solutions.
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