Ramaswamy, Mythily ; Unterreiter, Andreas (2004) Generalized Hardy-Sobolev inequalities and exponential decay of the entropy of g(x)u·=Δu Monatshefte für Mathematik, 143 (1). pp. 35-59. ISSN 0026-9255
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Official URL: http://www.springerlink.com/content/16acp9nkfcpcdm...
Related URL: http://dx.doi.org/10.1007/s00605-003-0041-6
Abstract
Provided the non-negative function g∈Lloc1(Ω) allows for a generalized Hardy-Sobolev inequality, existence and uniqueness of global weak solutions of the possibly degenerate parabolic PDE g(x)u·=Δu, subject to homogeneous Dirichlet boundary conditions, is proved. The maximum/minimum principle holds. The associated entropy decays exponentially as t ↑ ∞ with a rate not exceeding 2/C, where C is the constant arising in the generalized Hardy-Sobolev inequality.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Springer. |
| Keywords: | Hardy-Sobolev Inequality; Degenerate Parabolic PDE; Existence and Uniqueness of Global Solutions; Maximum Principle; Minimum Principle; Exponential Decay of Entropy |
| ID Code: | 62289 |
| Deposited On: | 20 Sep 2011 09:31 |
| Last Modified: | 20 Sep 2011 09:31 |
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