We investigate nonlinear diffusion equations with initial data and zero boundary conditions on bounded fractal domains. We show that these equations possess global solutions for suitable 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. 331–345DOI 10.4171/ZAA/1019