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We study the homogeneous Dirichlet problem for the doubly nonlinear equation$u_t = \Delta_p u^m$, where $p>1,\ m>0$ posed in a bounded domain in$\mathbb{R}^N$ with homogeneous boundary conditions and with non-negative andintegrable data. In this paper we consider the degenerate case $m(p-1)>1$ andthe quasilinear case $m(p-1)=1$. We establish the large-time behaviour byproving the uniform convergence to a unique asymptotic profile and we also giverates for this convergence.

Asymptotic behaviour of the doubly nonlinear equation $u_t=\Delta_p u^m$ on bounded domains