Abstract
We study the solutions with dead cores and the decay estimates for a parabolic p-Laplacian equation with absorption by sub- and supersolution method. Special attention is given to the case where the solution of the steady-state problem vanishes in an interior region.
Highlights
In this paper, we study the following initial-boundary value problem for u x,t : ut div u p 2 u = uq in Q =, (1.1)u0 x = x, x .The domain N N > 1 is smooth and bounded
We study the solutions with dead cores and the decay estimates for a parabolic p-Laplacian equation with absorption by sub- and supersolution method
Special attention is given to the case where the solution of the steady-state problem vanishes in an interior region
Summary
We study the following initial-boundary value problem for u x,t : ut div u p 2 u = uq in Q = ,. = O x with = p q 1 p , they showed that the solution converges as t to a self-similar solution. We have known the following behavior of the absorption near u = 0 :. Q < 1 strong absorption, q 1 weak absorption. U = 1 on D in [1], where D N be an arbitrary domain, a,b : D be two continuous functions, p 1 and f s is a nondecreasing function with f 0 = 0. From [1], we know that Problem (1.2) has a unique solution, a dead core exists if is large enough and. Are based on a suitable notion of weak solution, which we include here for the sake of completeness.
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