| Abstract: |
| In this talk, I consider a reaction-diffusion equation in a bounded interval of the real line with no-flux boundary conditions. In particular, the linear diffusion (typical of the classical reaction-diffusion models) is replaced by the (nonlinear) Perona-Malik diffusion and the reaction term is the derivative of a double well potential with wells of equal depth. After investigating the associated stationary problem and highlighting the differences with the standard results (linear diffusion), we focus the attention on the long time dynamics of solutions, proving either exponentially or algebraic slow motion of profiles with a transition layer structure. This is a joint work with Alessandra De Luca (University of Turin) and Marta Strani (University of Venice). |
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