A central limit theorem for solutions of the porous medium equation

✍ Scribed by Giuseppe Toscani

• Publisher: Springer
• Year: 2005
• Tongue: English
• Weight: 145 KB
• Volume: 5
• Category: Article
• ISSN: 1424-3199
• DOI: 10.1007/s00028-005-0183-1

✦ Synopsis

This paper is intended to study the large-time behavior of the second moment (energy)of solutions to the porous medium equation. As we shall briefly discuss in the following,the knowledge of the time evolution of the energy in a nonlinear diffusion equation is ofparamount importance to reckon the intermediate asymptotics of the solution itself whenthe similarity is missing. Thus, the present study can be considered as a first step in the validation of a more general conjecture on the large-time asymptotics of a general diffusion equation.