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
Related Articles
- EP ID EP539260
- DOI 10.15330/cmp.7.1.101-107
- Views 56
- Downloads 0
On the structure of least common multiple matrices from some class of matrices
For non-singular matrices with some restrictions, we establish the relationships between Smith normal forms and transforming matrices (a invertible matrices that transform the matrix to its Smith normal form) of two matr...
Mixed problem for the singular partial differential equation of parabolic type
The scheme for solving of a mixed problem is proposed for a differential equation a(x)∂T∂τ=∂∂x(c(x)∂T∂x)−g(x)T with coefficients a(x), g(x) that are the generalized derivatives of functions of bounded variation, c(x)>0,...
FG-coupled fixed point theorems in cone metric spaces
The concept of $FG$-coupled fixed point introduced recently is a generalization of coupled fixed point introduced by Guo and Lakshmikantham. A point $(x,y)\in X\times X$ is said to be a coupled fixed point of the mapping...
Index of pseudo-projectively-symmetric semi-Riemannian manifolds
The index of ˜∇-pseudo-projectively symmetric and in particular for ˜∇-projectively symmetric semi-Riemannian manifolds, where ˜∇ is Ricci symmetric metric connection, are discussed.
Advancement on the study of growth analysis of differential polynomial and differential monomial in the light of slowly increasing functions
Study of the growth analysis of entire or meromorphic functions has generally been done through their Nevanlinna's characteristic function in comparison with those of exponential function. But if one is interested to com...