Boundary-Value Problems for Ultraparabolic and Quasi-Ultraparabolic Equations with Alternating Direction of Evolution

被引：0
|
作者：
Kozhanov A.I. [1 ]
机构：
[1] Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
来源：
Journal of Mathematical Sciences | 2020年 / 250卷 / 5期
关键词：
35K70; 35M99; boundary-value problem; existence; odd-order nonclassical differential equation with alternating direction of evolution; regular solution; ultraparabolic equation; uniqueness;
D O I：
10.1007/s10958-020-05042-2
中图分类号：
学科分类号：
摘要：
We examine the solvability of boundary-value problems for the differential equationh(t)ut+(−1)mDa2m+1u−Δu+c(xta)u=f(xta);x∈Ω⊂ℝn,0<t<T,0<a<A,Dak=∂k∂ak, where the sign of the function h(t) arbitrarily alternates in the interval [0, T]. The existence and uniqueness theorems of regular (i.e., possessing all generalized derivatives in the Sobolev sense) solutions are proved. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.
引用
收藏
页码：772 / 779
页数：7
相关论文
共 50 条
12345