Extinction and Nonextinction for the Fast Diffusion Equation

Abstract EN

This paper deals with the extinction and nonextinction properties of the fast diffusion equation of homogeneous Dirichlet boundary condition in a bounded domain of RN with N>2.

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Furthermore, we prove that the solution either extinct or nonextinct in finite time depends strongly on the initial data and the first eigenvalue of -Δ with homogeneous Dirichlet boundary.