Asymptotic behaviour for the porous medium equation posed in the whole space
نویسنده
چکیده
with exponentm > 1, a range in which it is known as the porous medium equation, written here PME for short. The study extends the well-known theory of the classical heat equation (HE, the casem = 1) into a nonlinear situation, which needs a whole set of new tools. The space dimension can be any integer n ≥ 1. We will also present the extension of the results to exponents m < 1 (fast-diffusion equation, FDE). For definiteness we consider the Cauchy Problem posed inQ = R × R+ with initial data u(x, 0) = u0(x), x ∈ R (0.2)
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