American Institute of Mathematical Sciences

May  2020, 13(5): 1473-1493. doi: 10.3934/dcdss.2020083

Global existence for Laplace reaction-diffusion equations

 1 Department of Mathematics, Università degli Studi di Bologna, piazza di Porta S. Donato 5, 40126 Bologna, Italy 2 Professor Emeritus, Graduate School of Information Science and Technology, Osaka University, Suita, Osaka 565-0871, Japan

* Corresponding author: Atsushi Yagi

Received  June 2018 Revised  July 2018 Published  June 2019

We study the initial-boundary value problem for a Laplace reaction-diffusion equation. After constructing local solutions by using the theory of abstract degenerate evolution equations of parabolic type, we show global existence under suitable assumptions on the reaction function. We also show that the problem generates a dynamical system in a suitably set universal space and that this dynamical system possesses a Lyapunov function.

Citation: Angelo Favini, Atsushi Yagi. Global existence for Laplace reaction-diffusion equations. Discrete & Continuous Dynamical Systems - S, 2020, 13 (5) : 1473-1493. doi: 10.3934/dcdss.2020083
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