General asymptotic supnorm estimates for solutions of one-dimensional advection-diffusion equations in heterogeneous media, I
Jose A. Barrionuevo, Lucas S. Oliveira, Paulo. R. Zíngano
Abstract
We derive general bounds for the large time size of supnorm values of solutions to one-dimensional advection-diffusion equations with initial data in Lp0 (R) \cap L1 for some 1 <= p0 < \infty, and arbitrary bounded advection speeds b(x, t), introducing techniques based on suitable energy arguments. Some open problems and related results are also given.