On some perturbations of a stable process and solutions to the Cauchy problem for a class of pseudo-differential equations
Journal Title: Карпатські математичні публікації - Year 2015, Vol 7, Issue 1
Abstract
A fundamental solution for some class of pseudo-differential equations is constructed by the method based on the theory of perturbations. We consider a symmetric α-stable process in multidimensional Euclidean space. Its generator A is a pseudo-differential operator whose symbol is given by −c|λ|α, were the constants α∈(1,2) and c>0 are fixed. The vector-valued operator B has the symbol 2ic|λ|α−2λ. We construct a fundamental solution of the equation ut=(A+(a(⋅),B))u with a continuous bounded vector-valued function a.
Authors and Affiliations
M. M. Osypchuk
Keywords
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- EP ID EP539260
- DOI 10.15330/cmp.7.1.101-107
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