TY - JOUR
AU - Galina Tarasova
PY - 2022/02/01
Y2 - 2024/09/13
TI - On solvability of nonlocal boundary value problem for a differential equation of composite type
JF - Mathematical notes of NEFU
JA - Math. notes NEFU
VL - 28
IS - 4
SE - Mathematics
DO - https://doi.org/10.25587/SVFU.2021.27.62.007
UR - https://mzsvfu.ru/index.php/mz/article/view/on-solvability-of-nonlocal-boundary-value-problem-for-a-differential-equation
AB - We study the solvability in anisotropic Sobolev spaces of nonlocal in time problems for the differential equations of composite (Sobolev) type$$u_{tt}+\left(\alpha\frac{\partial}{\partial t}+\beta\right)\Delta u+\gamma u=f(x,t),$$$x = (x_1,\ldots , x_n) \in\Omega\subset R^n$, $t\in(0, T),$ $0 < T < +\infty$, $\alpha, \beta,$ and $\gamma$ are real numbers, and $f(x, t)$ is a given function. We prove theorems of existence and non-existence, uniqueness and non-uniqueness for regular solutions, those having all generalized Sobolev derivatives in the equation.
ER -