Du, Yihong; Lou, Bendong; Zhou, Maolin

Author(s)

Du, Yihong

Lou, Bendong

Zhou, Maolin

Publication Date

2016

Abstract

We classify the long-time behavior of solutions to nonlinear diffusive equations of the form ut − Δu = f(u) for t > 0 and x over a variable domain Ω(t) ⊂ ℝN, with a Stefan condition for u over the free boundary Γ(t) = ∂Ω(t), and u(0,x) > 0 in Ω(0) = Ω0. For monostable type of f and bistable type of f, we obtain a rather complete classification of the long-time dynamical behavior of the solution to this nonlinear Stefan problem, and examine how the behavior changes when u(0, x) takes initial functions of the form σφ(x) and σ > 0 is varied.

Citation

Journal of Elliptic and Parabolic Equations, 2(1), p. 297-321

ISSN

2296-9039

2296-9020

Link

https://hdl.handle.net/1959.11/20243

Publisher

Orthogonal Editions

Title

Spreading and Vanishing for Nonlinear Stefan Problems in High Space Dimensions

Type of document

Journal Article

Entity Type

Publication

Author(s)	Du, Yihong Lou, Bendong Zhou, Maolin
Publication Date	2016
Abstract	We classify the long-time behavior of solutions to nonlinear diffusive equations of the form ut − Δu = f(u) for t > 0 and x over a variable domain Ω(t) ⊂ ℝN, with a Stefan condition for u over the free boundary Γ(t) = ∂Ω(t), and u(0,x) > 0 in Ω(0) = Ω0. For monostable type of f and bistable type of f, we obtain a rather complete classification of the long-time dynamical behavior of the solution to this nonlinear Stefan problem, and examine how the behavior changes when u(0, x) takes initial functions of the form σφ(x) and σ > 0 is varied.
Citation	Journal of Elliptic and Parabolic Equations, 2(1), p. 297-321
ISSN	2296-9039 2296-9020
Link	https://hdl.handle.net/1959.11/20243
Publisher	Orthogonal Editions
Title	Spreading and Vanishing for Nonlinear Stefan Problems in High Space Dimensions
Type of document	Journal Article
Entity Type	Publication

Spreading and Vanishing for Nonlinear Stefan Problems in High Space Dimensions

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