Nonnegative solutions for a class of singular parabolic problems involving p-Laplacian

作者：de Bonis Ida; Giachetti Daniela^*

来源：Asymptotic Analysis, 2015, 91(2): 147-183.

DOI：10.3233/ASY-141257

• nonlinear parabolic equations
• singular lower order terms
• nonnegative solutions
• existence

We deal with the existence of nonnegative solutions to parabolic problems which are singular in the u variable whose model is
[GRAPHICES]
Here Omega is a bounded open subset of R-N, N >= 2, 0 < T < + infinity, theta > 0, Delta(p)u = div(|del u|(p-2)del u) with p > 1.
As far as the data are concerned, we assume f(x, t) is an element of L-r(0, T; L-m(Omega)), with 1/r + N/pm < 1, f(x, t) >= 0 a.e. in Omega x (0, T) and u(0)(x) >= 0 a.e. in Omega.
We consider also the case where the right-hand side depends on the gradient of the solution. In this last case the model of the right-hand side is F(x, t, u, del u) = f(x, t)+D|del u|(q)/u(theta), with theta > 0, D > 0, 1 < q < p and f(x, t) as before.

• 出版日期2015