Fundamental solution for Cauchy initial value problem for parabolic PDEs with discontinuous unbounded first-order coefficient at the origin. Extension of the classical parametrix method
Analysis of PDEs
2019-06-17 v1
Abstract
We prove the existence of a fundamental solution of the Cauchy initial boundary value problem on the whole space for a parabolic partial differential equation with discontinuous unbounded first-order coefficient at the origin. We establish also non-asymptotic, rapidly decreasing at infinity, upper and lower estimates for the fundamental solution. We extend the classical parametrix method provided by E.E. Levi.
Keywords
Cite
@article{arxiv.1906.05880,
title = {Fundamental solution for Cauchy initial value problem for parabolic PDEs with discontinuous unbounded first-order coefficient at the origin. Extension of the classical parametrix method},
author = {Maria Rosaria Formica and Eugeny Ostrovsky and Leonid Sirota},
journal= {arXiv preprint arXiv:1906.05880},
year = {2019}
}