(untitled) (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) ∈ R × (0, +∞) with initial condition u(x, 0) = u_0(x) x ∈ (-∞, +∞), where μ(x) is a nonnegative finite Radon measure, u_0 ∈ L¹(R) ∩ L∞(R) is a nonnegative function, and m > 1, and R ≡ (-∞, +∞).