Maria Assunta Pozio

Support properties of solutions for a class of degenerate parabolic problems

On considere les proprietes qualitatives des solutions du probleme de Cauchy-Dirichlet suivant: ∂ t u=Δφ(u)+uf(x,u) dans (0,∞)×Ω; u=0 dans (0,∞)×∂Ω, u=u 0 dans {0}×Ω; ou Ω⊂R d est un ouvert borne a frontiere lisse ∂Ω

Degenerate parabolic Problems in population dynamics

We investigate the coexistence of prey-predator or competing species, subject to density dependent diffusion in an inhomogeneous habitat. It is proven that coexistence arises in suitable domains, where favourable conditions are satisfied. Support properties and attractivity of the resulting stationary solutions are investigated.

Sublinear elliptic problems with a Hardy potential

In this paper we study the positive solutions of sub linear elliptic equations with a Hardy potential which is singular at the boundary. By means of ODE techniques a fairly complete picture of the class of radial solutions is given. Local solutions with a prescribed growth at the boundary are constructed by means of contraction operators. Some of those radial solutions are then used to construct ordered upper and lower solutions in general domains. By standard iteration arguments the existence of positive solutions is proved. An important tool is the Hardy constant.

On a class of nonlinear Neumann problems

SummaryExistence theorems for nonlinear Neumann problems with inhomogeneous boundary conditions are established. It is then investigated under which conditions the solutions are uniformly bounded. Uniqueness results for positive solutions are given and the asymptotic behavior of the solutions of the corresponding parabolic equation is discussed. The main tools are fixed point theorems and the method of upper and lower solutions.

Nonlinear Parabolic Equations with Sinks and Sources

Let D ⊂R N be a bounded domain whose boundary is in C 1. We shall put

Criteria for well-posedness of degenerate elliptic and parabolic problems

{Q_T}: = D \times \left( {0,T} \right)\quad and\quad {\Gamma_T}: = \partial D \times \left( {0,T} \right)

The Fujita exponent for the Cauchy problem in the hyperbolic space

. Suppose that a(x) ∈ C α (D), α ∈ (0, 1], is an arbitrary function of variable sign and that u 0 (x) ≥ 0 is continuous in D.