TY - JOUR
AU - Horodets'kyi, V.V.
AU - Martynyuk, O.V.
PY - 2021/06/28
Y2 - 2024/07/19
TI - Evolution pseudodifferential equations with analytic symbols in spaces of $S$ type
JF - Carpathian Mathematical Publications
JA - Carpathian Math. Publ.
VL - 13
IS - 1
SE - Scientific articles
DO - 10.15330/cmp.13.1.160-179
UR - https://journals.pnu.edu.ua/index.php/cmp/article/view/4359
SP - 160-179
AB - <p>A nonlocal multipoint by time problem for an evolution equation with a pseudodifferential operator is studied. This operator is treated as an infinite order differentiation operator in generalized spaces of $S$ type. We consider the case when the initial condition of the problem is an element of an ultradistributions type space and the nonlocial condition contains pseudodifferential operators. The solvability of such problem is established, the properties of the fundamental solution are investigated, the analytical representation of the solution is found.</p>
ER -