Asymptotic Behavior of Nonlinear Diffusions
نویسندگان
چکیده
for a given initial data u(x, 0) = u0(x) ≥ 0, where p > 1 and N ≥ 2. Such a solution exists and it is unique in the natural weak sense under rather mild conditions on u0. In particular, this is the case for u0 ∈ L , condition which we will assume in what follows. We refer the reader to [11,10] for general results on the issues of existence, uniqueness and regularity of non-negative solutions. It is known that a fundamental solution of (1) exists whenever p > 2N/(N+1). This is a non-negative solution of (1) which takes a Dirac mass Mδ0, M > 0, as initial data. It is unique, see [14], and explicitly given by
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