By Dr. Oscar Jarrín. Universidad de las Américas, Quito.
Fecha seminario: 2022-06-02
In this talk, we consider a heat equation with the natural polynomial non-linear term; and with two different cases in the diffusion term. The first case (anomalous diffusion) concerns the fractional Laplacian operator with parameter between 1 and 2, while the second case (classical diffusion) involves the classical Laplacian operator. When a tends to 2, we prove the uniform convergence of the solutions of the anomalous diffusion case to a solution of the classical diffusion case. Moreover, we rigorous derive a convergence rate, which was numerically exhibit in previous related works.