Heat equations with fast convection: source-type solutions and large-time behaviour
Analysis of PDEs
2023-03-06 v1
Abstract
We study the existence and uniqueness of source-type solutions to the Cauchy problem for the heat equation with fast convection under certain tail control assumptions. We allow the solutions to change sign, but we will in fact show that they have the same sign as the initial data, which is a multiple of the Dirac delta. As an application, we obtain the large-time behaviour of nonnegative bounded solutions with integrable initial data to heat equations with fast convection, covering the case of several dimensions that remained open since the end of last century.
Cite
@article{arxiv.2303.01908,
title = {Heat equations with fast convection: source-type solutions and large-time behaviour},
author = {Jørgen Endal and Liviu I. Ignat and Fernando Quirós},
journal= {arXiv preprint arXiv:2303.01908},
year = {2023}
}
Comments
15 pages