Abstract
In this paper, we investigate a reaction–diffusion equation with a Caputo fractional derivative in time and with boundary conditions. According to the principle of contraction mapping, we first prove the existence and uniqueness of local solutions. Then, under some conditions of the initial data, we obtain two sufficient conditions for the blow-up of the solutions in finite time. Moreover, the existence of global solutions is studied when the initial data is small enough. Finally, the long-time behavior of bounded solutions is analyzed.
Funder
The Joint Special Funds of the Basic Research Foundation of Yunnan Province
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Reference31 articles.
1. Fractional Integrals and Derivatives, Theory and Applications;Samko,1993
2. Fractional Differential Equations;Podlubny,1998
3. Theory and Applications of Fractional Differential Equations;Kilbas,2006
4. Invariant analysis and explicit solutions of the time fractional nonlinear perturbed Burgers equation
5. On New Existence Results for Fractional Differential Equations in Quaternionic Analysis
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献