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.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.