TY - JOUR

T1 - Degenerating parabolic equations with a variable direction of evolution

AU - Kozhanov, Alexandr Ivanovich

AU - Macievskaya, Ekaterina Evgenievna

PY - 2019/1/1

Y1 - 2019/1/1

N2 - The aim of the paper is to study the solvability in the classes of regular solutions of boundary value problems for differential equations ϕ (t)ut - ψ (t)Δu + c(x, t)u = f(x, t) (x ∈ Ω ⊂ ℝn, 0 < t < T). A feature of these equations is that the function ϕ(t) in them can arbitrarily change the sign on the segment [0, T], while the function ψ (t) is nonnegative for t ∈ [0, T]. For the problems under consideration, we prove existence and uniqueness theorems.

AB - The aim of the paper is to study the solvability in the classes of regular solutions of boundary value problems for differential equations ϕ (t)ut - ψ (t)Δu + c(x, t)u = f(x, t) (x ∈ Ω ⊂ ℝn, 0 < t < T). A feature of these equations is that the function ϕ(t) in them can arbitrarily change the sign on the segment [0, T], while the function ψ (t) is nonnegative for t ∈ [0, T]. For the problems under consideration, we prove existence and uniqueness theorems.

KW - Boundary value problems

KW - Degenerate parabolic equations

KW - Existence

KW - Regular solutions

KW - Uniqueness

KW - Variable direction of evolution

KW - degenerate parabolic equations

KW - variable direction of evolution

KW - boundary value problems

KW - regular solutions

KW - existence

KW - uniqueness

UR - http://www.scopus.com/inward/record.url?scp=85071176175&partnerID=8YFLogxK

UR - https://www.elibrary.ru/item.asp?id=42735092

U2 - 10.33048/semi.2019.16.048

DO - 10.33048/semi.2019.16.048

M3 - Article

AN - SCOPUS:85071176175

VL - 16

SP - 718

EP - 731

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

ER -