Non-delay limit in the energy space from the nonlinear damped wave equation to the nonlinear heat equation

Abstract

We consider a singular limit problem from the damped wave equation with a power type nonlinearity (NLDW) to the corresponding heat equation (NLH). We call our singular limit problem non-delay limit. We show that the solution of NLDW goes to the one of NLH in [Formula: see text] topology under the both [Formula: see text] regularity solutions. We also obtain the positive convergence rate in the weaker topology [Formula: see text]. Moreover, with restriction of the range of power, if the solution to NLH is global and decays to zero, then we get the global-in-time uniform convergence of the non-delay limit.