Existence and Uniqueness of BV Solutions for the Porous Medium Equation with Dirac Measure as Sources (Journal of Partial Differential Equations, 2005)
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} ≡ (-∞, +∞).