科研之友
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摘要
We study the initial value problem with unbounded nonnegative functions or measures for the equation partial derivative(t)u - Delta(p)u + f(u) = 0 in R-N x (0, infinity) where p %26gt; 1, Delta(p)u = div(|del|(p-2) del u) and f is a continuous, nondecreasing nonnegative function such that f(0) = 0. In the case p %26gt; 2N/N+1 , we provide a sufficient condition on f for existence and uniqueness of the solutions satisfying the initial data k delta(0) and we study their limit when k -%26gt; infinity according f(-1) and F-1/p are integrable or not at infinity, where F(s) = integral(8)(0) f(sigma)d sigma. We also give new results dealing with uniqueness and non uniqueness for the initial value problem with unbounded initial data. If p %26gt; 2, we prove that, for a large class of nonlinearities f, any positive solution admits an initial trace in the class of positive Borel measures. As a model case we consider the case f(u) = u(alpha) ln(beta)(u + 1), where alpha %26gt; 0 and beta %26gt;= 0.
- 出版日期2013-5
