The filtration equation in a class of functions decreasing at infinity
Daniel Eidus, Shoshana Kamin · Proceedings of the American Mathematical Society · 1994
We deal with the Cauchy and external boundary problems for the nonlinear filtration equation with variable density. For each density we define a class ϕ \phi of initial functions φ \varphi , such that for any φ ∈ ϕ \varphi \in \phi the problem is uniquely solvable in some set of functions decreasing at infinity with respect to space variables.