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
Continuous block-symmetric polynomials of degree at most two on the space $(L_\infty)^2$
We introduce block-symmetric polynomials on $(L_\infty)^2$ and prove that every continuous block-symmetric polynomial of degree at most two on $(L_\infty)^2$ can be uniquely represented by some "elementary" block-symmetr...
On properties of the solutions of the Weber equation
Growth, convexity and the l-index boundedness of the functions α(z) and β(z), such that α(z4) and zβ(z4) are linear independent solutions of the Weber equation w′′−(z24−ν−12)w=0 if ν=−12 are investigated.
Application of duality theory to solve two-criteria problem of linear programming for ecological-economic system
In the paper, we investigate two-criterion optimization problem: maximization of one target function and minimization of another target function. To solve the offered two-criterion problem, the method of the main criteri...
Generalized types of the growth of Dirichlet series
Let A∈(−∞,+∞] and Φ be a continuously on [σ0,A) function such that Φ(σ)→+∞ as σ→A−0. We establish a necessary and sufficient condition on a nonnegative sequence λ=(λn), increasing to +∞, under which the equality ¯¯¯¯¯¯¯¯...
On nonlocal boundary value problem for the equation of motion of a homogeneous elastic beam with pinned-pinned ends
In the current paper, in the domain D={(t,x):t∈(0,T),x∈(0,L)} we investigate the boundary value problem for the equation of motion of a homogeneous elastic beam utt(t,x)+a2uxxxx(t,x)+buxx(t,x)+cu(t,x)=0, where a,b,c∈R,...