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 - <p>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 &gt; 1, and \mathbb{R} ≡ (-∞, +∞).</p>