Solvability to some strongly degenerate parabolic problems

Результат исследования: Научные публикации в периодических изданияхстатьярецензирование


Nonlinear parabolic equations of “divergence form,” u t =(φ(u)ψ(u x )) x , are considered under the assumption that the “material flux,” φ(u)ψ(v), is bounded for all values of arguments, u and v. In literature such equations have been referred to as “strongly degenerate” equations. This is due to the fact that the coefficient, φ(u)ψ (u x ), of the second derivative, u xx , can be arbitrarily small for large value of the gradient, u x . The “hyperbolic phenomena” (unbounded growth of space derivatives within a finite time) have been established in literature for solutions to Cauchy problem for the above-mentioned equations. Accordingly one can expect a correct statement of the initial-boundary value problem for such equations only under additional assumptions on the problem data. In this paper we describe several restrictions, under which the initial-boundary value problems for strongly degenerate parabolic equations are well-posed.

Язык оригиналаанглийский
Страницы (с-по)576-594
Число страниц19
ЖурналJournal of Mathematical Analysis and Applications
Номер выпуска1
СостояниеОпубликовано - 1 июл. 2019


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