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

页码：772 / 779

页数：7

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