LONG TIME BEHAVIOUR OF SOLUTIONS TO AN EVOLUTION PDE WITH NONSTANDARD GROWTH

Hélène Frankowska (1) , Gioconda Moscariello

1 IMJ - Institut de Mathématiques de Jussieu

In this paper we prove time estimates for solutions to a general nonhomo-geneous parabolic problem whose operator satisfies nonstandard growth conditions. We also study the asymptotic behaviour of solutons to an anisotropic problem.

Mots clés: Evolution PDE; time dependence of solutions at infinity; generalized Gronwall lemma Mathematics Subject Classification 35K51; 35K59; 35B40

Domaines: Mathématiques [math]; Equations aux dérivées partielles [math.AP]

Hélène Frankowska, Gioconda Moscariello. LONG TIME BEHAVIOUR OF SOLUTIONS TO AN EVOLUTION PDE WITH NONSTANDARD GROWTH. Advances in Calculus of Variation, 2020, ⟨10.1515/acv-2019-0061⟩. ⟨hal-02906911⟩