Existence and Uniqueness of BV Solutions for the Porous Medium Equation with Dirac Measure as Sources
Year: 2005
Journal of Partial Differential Equations, Vol. 18 (2005), Iss. 1 : pp. 35–58
Abstract
The aim of this paper is to discuss the existence and uniqueness of solutions for the porous medium equation u_t - (u^m)_{xx} = μ(x) in (x, t) ∈ \mathbb{R} × (0, +∞) with initial condition u(x, 0) = u_0(x) x ∈ (-∞, +∞), where μ(x) is a nonnegative finite Radon measure, u_0 ∈ L¹(\mathbb{R}) ∩ L∞(\mathbb{R}) is a nonnegative function, and m > 1, and \mathbb{R} ≡ (-∞, +∞).
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2005-JPDE-5344
Journal of Partial Differential Equations, Vol. 18 (2005), Iss. 1 : pp. 35–58
Published online: 2005-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: BV solution