In this work, the behaviour of solutions for the Dirichlet problem of the non-local equation u(t) = Delta(kappa(u)) + lambdaf(u)/(integral(Omega)f(u) dx)(p) , Omega subset of R-N, N = 1, 2, is studied, mainly for the case where f(s) = e(kappa)((s)). More precisely, the interplay of exponent p of the non-local term and spatial dimension N is investigated with regard to the existence and non-existence of solutions of the associated steady-state problem as well as the global existence and finite-time blow-up of the time-dependent solutions u(x, t). The asymptotic stability of the steady-state solutions is also studied.
展开▼
