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The one-dimensional nonlinear heat-equation with absorption: regularity of solutions and interfaces

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Herrero, Miguel A. and Vázquez, Juan Luis (1987) The one-dimensional nonlinear heat-equation with absorption: regularity of solutions and interfaces. Siam Journal on Mathematical Analysis, 18 (1). pp. 149-167. ISSN 0036-1410

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Official URL: http://epubs.siam.org/simax/resource/1/sjmaah/v18/i1/p149_s1?isAuthorized=no


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Abstract

We consider the equation ut=(Um)xx-λun with m>1, λ>0, n≥m as a model for heat diffusion with absorption. Hence we assume that u≥0 for xЄR, t≥0. We study the regularity of the solution to the Cauchy problem for this degenerate parabolic equation. When the initial datum uo(X)is positive only in a part of the space R, we also study the regularity of the free boundaries that appear. The asymptotic behavior of solutions and free boundaries is also discussed.


Item Type:Article
Uncontrolled Keywords:Nonlinear diffusion with absorption, regularity, interfaces or free boundaries, waiting time, asymptotic behavior
Subjects:Sciences > Mathematics > Differential equations
ID Code:17602
Deposited On:10 Jan 2013 09:40
Last Modified:12 Dec 2018 15:08

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