JournalszaaVol. 20, No. 2pp. 331–345

Nonlinear Diffusion Equations on Bounded Fractal Domains

  • Jiaxin Hu

    Tsinghua University, Beijing, China
Nonlinear Diffusion Equations on Bounded Fractal Domains cover
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Abstract

We investigate nonlinear diffusion equations ut=Δ¢u+f(u)\frac {\partial u}{\partial t} = \Delta ¢u +f(u) with initial data and zero boundary conditions on bounded fractal domains. We show that these equations possess global solutions for suitable ff and small initial data by employing the iteration scheme and the maximum principle that we establish on the bounded fractals under consideration. The Sobolev-type inequality is the starting point of this work, which holds true on a large class of bounded fractal domains and gives rise to an eigenfunction expansion of the heat kernel.

Cite this article

Jiaxin Hu, Nonlinear Diffusion Equations on Bounded Fractal Domains. Z. Anal. Anwend. 20 (2001), no. 2, pp. 331–345

DOI 10.4171/ZAA/1019