A free-boundary problem for the evolution p-Laplacian equation with a combustion boundary condition

To, Tung
June 2009
Calculus of Variations & Partial Differential Equations;Jun2009, Vol. 35 Issue 2, p239
Academic Journal
We study the existence, uniqueness and regularity of solutions of the equation f t = ? p f = div (| Df| p-2 Df) under over-determined boundary conditions f = 0 and | Df| = 1. We show that if the initial data is concave and Lipschitz with a bounded and convex support, then the problem admits a unique solution which exists until vanishing identically. Furthermore, the free-boundary of the support of f is smooth for all positive time.


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