Anisotropic parabolic problems with slowly or rapidly growing terms

• Autorzy: Agnieszka Świerczewska-Gwiazda
• Języki publikacji: EN

Abstrakty

EN

We consider an abstract parabolic problem in a framework of maximal monotone graphs, possibly multi-valued, with growth conditions formulated with the help of an x-dependent N-function. The main novelty of the paper consists in the lack of any growth restrictions on the N-function combined with its anisotropic character, namely we allow the dependence on all the directions of the gradient, not only on its absolute value. This leads to using the notion of modular convergence and studying in detail the question of density of compactly supported smooth functions with respect to modular convergence.

Kategorie tematyczne

• 35K20: Initial-boundary value problems for second-order parabolic equations
• 35K55: Nonlinear parabolic equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2014
• Tom: 134
• Numer: 1
• Strony: 113-130

Daty

wydano

2014

Twórcy

autor

Agnieszka Świerczewska-Gwiazda

• Institute of Applied Mathematics and Mechanics, University of Warsaw, 02-097 Warszawa, Poland

Identyfikatory

DOI

10.4064/cm134-1-5