Refined estimates for the propagation speed of the transition solution to a free boundary problem with a nonlinearity of combustion type

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:265

Article

Lei, Chengxia¹  Matsuzawa, Hiroshi²  Peng, Rui¹  Zhou, Maolin³ 

[1] Jiangsu Normal Univ, Sch Math & Stat, Xuzhou 221116, Jiangsu, Peoples R China

[2] Numazu Coll, Natl Inst Technol, 3600 Ooka, Numazu, Shizuoka 4108501, Japan

[3] Univ New England, Sch Sci & Technol, Armidale, NSW 2351, Australia

关键词: Free boundary problem;    Nonlinear diffusion equation;    Combustion;    Propagation speed;   

DOI  :  10.1016/j.jde.2018.04.053

来源: Elsevier

【 摘 要 】

We are concerned with the nonlinear problem u(t) = u(xx) f (u), where f is of combustion type, coupled with the Stefan-type free boundary h(t). According to [4,5], for some critical initial data, the transition solution u locally uniformly converges to theta, which is the ignition temperature of f , and the free boundary satisfies h(t) = C root t + o(1). root t for some positive constant C and all large time t. In this paper, making use of two different approaches, we establish more accurate upper and lower bound estimates on h(t) for the transition solution, which suggest that the nonlinearity f can essentially influence the propagation speed. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free