|
|||||
|
|
Decay of global solutions, stability and blowup for a reaction-diffusion problem with free boundary |
|
| Authors: | Hamid Ghidouche Philippe Souplet Domingo Tarzia |
| Institution: | Laboratoire Analyse, Géométrie et Applications, UMR CNRS 7539, Institute Galilée, Université Paris Nord, 93430 Villetaneuse, France Philippe Souplet ; Département de Mathématiques, Université de Picardie, INSSET, 02109 St-Quentin, France and Laboratoire de Mathématiques Appliquées, UMR CNRS 7641, Université de Versailles 45 avenue des Etats-Unis, 78302 Versailles, France ; Departamento de Matemática, FCE, Universidad Austral, Paraguay 1950, 2000, Rosario, Argentina |
| Abstract: | We consider a one-phase Stefan problem for the heat equation with a nonlinear reaction term. We first exhibit an energy condition, involving the initial data, under which the solution blows up in finite time in |
| Keywords: | Nonlinear reaction-diffusion equation free boundary condition Stefan problem global existence boundedness of solutions decay stability finite time blow up |
| 点击此处可从《Proceedings of the American Mathematical Society》浏览原始摘要信息 | |
| 点击此处可从《Proceedings of the American Mathematical Society》下载免费的PDF全文 | |
norm. We next prove that all global solutions are bounded and decay uniformly to 0, and that either: (i) the free boundary converges to a finite limit and the solution decays at an exponential rate, or (ii) the free boundary grows up to infinity and the decay rate is at most polynomial. Finally, we show that small data solutions behave like (i).