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

Maria Rosaria Formica; Eugeny Ostrovsky; Leonid Sirota

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arXiv · 1906.05880

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

Maria Rosaria Formica·Eugeny Ostrovsky·Leonid Sirota

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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.

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Maria Rosaria Formica, Eugeny Ostrovsky, Leonid Sirota. 2019-06-13. 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. https://arxiv.org/abs/1906.05880

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