TY - JOUR
AU - Osypchuk, M.M.
PY - 2015/07/03
Y2 - 2024/05/18
TI - On some perturbations of a stable process and solutions to the Cauchy problem for a class of pseudo-differential equations
JF - Carpathian Mathematical Publications
JA - Carpathian Math. Publ.
VL - 7
IS - 1
SE - Scientific articles
DO - 10.15330/cmp.7.1.101-107
UR - https://journals.pnu.edu.ua/index.php/cmp/article/view/1388
SP - 101-107
AB - <p>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 $\alpha$-stable process in multidimensional Euclidean space. Its generator $\mathbf{A}$ is a pseudo-differential operator whose symbol is given by $-c|\lambda|^\alpha$, were the constants $\alpha\in(1,2)$ and $c>0$ are fixed. The vector-valued operator $\mathbf{B}$ has the symbol $2ic|\lambda|^{\alpha-2}\lambda$. We construct a fundamental solution of the equation $u_t=(\mathbf{A}+(a(\cdot),\mathbf{B}))u$ with a continuous bounded vector-valued function $a$.</p>
ER -