On a fractional thin film equation

Advances in Nonlinear Analysis

Segatti Antonio¹  Vázquez Juan Luis² 

[1] Dipartimento di Matematica “F. Casorati", Università di Pavia, Via Ferrata 1, 27100, Pavia, Italy;Matemáticas, Universidad Autónoma de Madrid, Campus de Cantoblanco, 28049, Madrid, Spain;

关键词: fractional operators;    thin film equations;    self-similar solutions;    obstacle problem;    35r11;    35g25;    35k46;    35k65 35c06;   

DOI  :  10.1515/anona-2020-0065

来源: DOAJ

【 摘 要 】

This paper deals with a nonlinear degenerate parabolic equation of order α between 2 and 4 which is a kind of fractional version of the Thin Film Equation. Actually, this one corresponds to the limit value α = 4 while the Porous Medium Equation is the limit α = 2. We prove existence of a nonnegative weak solution for a general class of initial data, and establish its main properties. We also construct the special solutions in self-similar form which turn out to be explicit and compactly supported. As in the porous medium case, they are supposed to give the long time behaviour or the wide class of solutions. This last result is proved to be true under some assumptions.

【 授权许可】

Unknown