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Volume 18, Issue 1
Existence and Uniqueness of BV Solutions for the Porous Medium Equation with Dirac Measure as Sources

Hongjun Yuan & Yang Jin

J. Part. Diff. Eq., 18 (2005), pp. 35-58.

Published online: 2005-02

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  • 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} ≡ (-∞, +∞).

  • Keywords

BV solution porous medium equation existence and uniqueness

  • AMS Subject Headings

35K45 35K55 35K65.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-18-35, author = {}, title = {Existence and Uniqueness of BV Solutions for the Porous Medium Equation with Dirac Measure as Sources}, journal = {Journal of Partial Differential Equations}, year = {2005}, volume = {18}, number = {1}, pages = {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} ≡ (-∞, +∞).

}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5344.html} }
TY - JOUR T1 - Existence and Uniqueness of BV Solutions for the Porous Medium Equation with Dirac Measure as Sources JO - Journal of Partial Differential Equations VL - 1 SP - 35 EP - 58 PY - 2005 DA - 2005/02 SN - 18 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5344.html KW - BV solution KW - porous medium equation KW - existence and uniqueness AB -

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} ≡ (-∞, +∞).

Hongjun Yuan & Yang Jin . (2019). Existence and Uniqueness of BV Solutions for the Porous Medium Equation with Dirac Measure as Sources. Journal of Partial Differential Equations. 18 (1). 35-58. doi:
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