### Asymptotic limits for the doubly nonlinear equation

M. Astudillo

#### Abstract

This article is concerned with the asymptotic limits of the solutions of the homogeneous Dirichlet problem associated to a doubly nonlinear evolution equation of the form $u_{t} = \Delta_{p}u^{m} + g$, in a bounded domain, as the parameters $p$ and $m$ tend to infinity. We will address the limits in $p$ and $m$ separately and in sequence, eventually completing a convergence diagram for this problem. We prove, under additional assumptions on the domain and initial data, that the equation satisfied at the limit is independent of the order in which we take the limits in $p$ and $m$.

#### Article information

Source
Adv. Differential Equations, Volume 19, Number 7/8 (2014), 613-634.

Dates
First available in Project Euclid: 6 May 2014