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On a class of nonlinear degenerate parabolic equations

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Herrero, Miguel A. (1982) On a class of nonlinear degenerate parabolic equations. Portugaliae mathematica, 41 (1-4). pp. 261-268. ISSN 0032-5155

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Abstract

The paper is a nice brief review of fundamental results about the initial value problem for one-dimensional nonlinear degenerate parabolic equations of "porous media'' type: ut=[φ(ux)]x, x∈R, t>0, with φ continuous, nondecreasing, φ(0)=0, |φ(s)|→∞ as |s|→∞. The results concern existence, uniqueness and regularity of solutions with initial data u0 in L2 (u0 not necessarily of one sign). When u0≥0 has compact support, regularity and growth results of the interfaces demarcating the compact support of the solution are also described.


Item Type:Article
Uncontrolled Keywords:Existence; uniqueness; generalized solutions; regularity; propagation properties; behavior of interfaces
Subjects:Sciences > Mathematics > Differential equations
ID Code:22740
Deposited On:09 Sep 2013 15:50
Last Modified:12 Dec 2018 15:08

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