TY - JOUR
AU - Aleksandr Kozhanov
AU - Galina Lukina
PY - 2021/10/07
Y2 - 2022/01/17
TI - Degeneration in differential equations with multiple characteristics
JF - Mathematical notes of NEFU
JA - Math. notes NEFU
VL - 28
IS - 3
SE - Mathematics
DO - https://doi.org/10.25587/SVFU.2021.91.97.002
UR - https://mzsvfu.ru/index.php/mz/article/view/degeneration-in-differential-equations-with-multiple-characteristics
AB - We study the solvability of boundary value problems for the differential equations$$\varphi(t)u_t+(-1)^m\psi(t)D^{2m+1}_{x}u+c(x,t)u=f(x,t),$$$$\varphi(t)u_{tt}+(-1)^{m+1}\psi(t)D^{2m+1}_{x}u+c(x,t)u=f(x,t),$$where $x\in(0, 1)$, $t\in(0, T),$ $m$ is a non-negative integer, $D^k_x=\frac{\partial^k}{\partial x^k}$ ($D^1_x=D_x$), while the functions $\varphi(t)$ and $\psi(t)$ are non-negative and vanish at some points of the segment $[0, T]$. We prove the existence and uniqueness theorems for the regular solutions, those having all generalized Sobolev derivatives required in the equation, in the inner subdomains.
ER -