Slow growth of solutions of super-fast diffusion equations with\n unbounded initial data

2016/05/13 by Марек Фила, Michael Winkler, Fila, Marek +1 · 1 citation
Mathematics · Medicine · Physics and Astronomy · #35B40 #35C06 #35K55 #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1605.04150

openalex publication_date 2016/05/13 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

We study positive solutions of the super-fast diffusion equation in the whole\nspace with initial data which are unbounded as |x|\→\∞. We find an\nexplicit dependence of the slow temporal growth rate of solutions on the\ninitial spatial growth rate. A new class of self-similar solutions plays a\nsignificant role in our analysis.\n

Cited by

• Asymptotic large time behavior of singular solutions of the fast diffusion equation

Related

• Vanishing time behavior of solutions to the fast diffusion equation
• Asymptotic large time behavior of singular solutions of the fast diffusion equation
• Positivity, local smoothing, and Harnack inequalities for very fast diffusion equations
• Global behaviour of solutions of the fast diffusion equation
• Uniqueness and time oscillating behaviour of finite points blow-up\n solutions of the fast diffusion equation