Degenerating parabolic equations with a variable direction of evolution

Alexandr Ivanovich Kozhanov, Ekaterina Evgenievna Macievskaya

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

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.

Translated title of the contributionВырождающиеся параболические уравнения с переменным направлением эволюции
Original languageEnglish
Pages (from-to)718-731
Number of pages14
JournalСибирские электронные математические известия
Volume16
DOIs
Publication statusPublished - 1 Jan 2019

Keywords

  • degenerate parabolic equations
  • variable direction of evolution
  • boundary value problems
  • regular solutions
  • existence
  • uniqueness

OECD FOS+WOS

  • 1.01 MATHEMATICS

State classification of scientific and technological information

  • 27 MATHEMATICS

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