A nonlinear Stefan problem with variable exponent and different moving parameters

Huiling Li; Xiaoliu Wang; Xueyan Lu

doi:10.3934/dcdsb.2019246

Article Contents

2020, Volume 25, Issue 5: 1671-1698. Doi: 10.3934/dcdsb.2019246

This issue Previous Article A free boundary problem for a prey-predator model with degenerate diffusion and predator-stage structure Next Article Influence of feedback controls on the global stability of a stochastic predator-prey model with Holling type Ⅱ response and infinite delays

A nonlinear Stefan problem with variable exponent and different moving parameters

School of Mathematics, Southeast University, Nanjing 210096, China

^* Corresponding author: Huiling Li
^* Corresponding author: Huiling Li

Received: March 31, 2019

Revised: May 31, 2019

Early access: November 2019

Published: May 2020

The work is supported by NSFC Grants 11171064 and 11871148, and by the Natural Science Foundation of Jiangsu Province BK20161412

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Abstract

In this paper, we consider a nonlinear diffusion problem with variable exponent, accompanied by double free boundaries possessing different moving parameters, where the variable exponent function $ m(x) $ satisfies that $ m(x)-1 $ can change its sign. Local existence and uniqueness of solution are established firstly, and then, some sufficient conditions are achieved for finite time blowup, and as well for global existence. Asymptotic behavior is further investigated for global solution, and existences of fast solution and slow solution are presented by making use of upper-sub solutions, energy and scaling arguments.

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Mathematics Subject Classification: Primary: 35A01, 35A02, 35B09, 35B44, 35B50, 35B51, 35G25, 35R35.

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