scholarly journals Long-time behavior of stochastic reaction-diffusion equation with dynamical boundary condition

2017 ◽  
Vol 22 (7) ◽  
pp. 2627-2650 ◽  
Author(s):  
Lu Yang ◽  
◽  
Meihua Yang ◽  
Keyword(s):  
Boundary Condition ◽  
Diffusion Equation ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Dynamical Boundary Condition ◽  
Long Time ◽  
Stochastic Reaction

scholarly journals Blow-Up and Global Existence of Solutions for the Time Fractional Reaction–Diffusion Equation

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3248
Author(s):  
Linfei Shi ◽  
Wenguang Cheng ◽  
Jinjin Mao ◽  
Tianzhou Xu
Keyword(s):  
Initial Data ◽  
Diffusion Equation ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Global Solutions ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Time Behavior ◽  
Global Existence Of Solutions ◽  
Long Time

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.

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