Per ogni soluzione della (1) nel dominio limitato $\mathrm{\Omega }$,, appartenente a $H_0^2(\mathrm{\Omega })$ e soddisfacente le condizioni (2), si dimostra la maggiorazione (5), valida nell'intorno di ogni punto $x^0$ del contorno; si consente a $\partial \mathrm{\Omega }$ di essere singolare in $x^0$.

We are very interested with asymptotic problems for the system of elasticity involving small parameters in the description of the domain where the solutions is searched. The corresponding asymptotic expansions have different forms in the various between them. More precisely, our work is concerned with a precise description of the deformation and the stress fields at the junction of an elastic three-dimensional body and a cylinder. The corresponding small parameter is the diameter of the cylinder....

We consider a model of migrating population occupying a compact domain Ω in the plane. We assume the Malthusian growth of the population at each point x ∈ Ω and that the mobility of individuals depends on x ∈ Ω. The evolution of the probability density u(x,t) that a randomly chosen individual occupies x ∈ Ω at time t is described by the nonlocal linear equation $u_t={\int }_{\Omega }\phi \left(y\right)u(y,t)dy-\phi \left(x\right)u(x,t)$, where φ(x) is a given function characterizing the mobility of individuals living at x. We show that the asymptotic behaviour of u(x,t)...

We consider the evolution of an entire convex graph in euclidean space with speed given by a symmetric function of the principal curvatures. Under suitable assumptions on the speed and on the initial data, we prove that the solution exists for all times and it remains a graph. In addition, after appropriate rescaling, it converges to a homothetically expanding solution of the flow. In this way, we extend to a class of nonlinear speeds the well known results of Ecker and Huisken for the mean curvature...

In this paper we study the boundary exact controllability for the equation $$\frac{\partial }{\partial t}\left(\alpha \left(t\right)\frac{\partial y}{\partial t}\right)-\sum _{j=1}^n\frac{\partial }{\partial x_j}\left(\beta \left(t\right)a\left(x\right)\frac{\partial y}{\partial x_j}\right)=0\text{in}\Omega \times (0,T),$$ when the control action is of Dirichlet-Neumann form and $\Omega$ is a bounded domain in $R^n$. The result is obtained by applying the HUM (Hilbert Uniqueness Method) due to J. L. Lions.

The present paper studies the existence and uniqueness of global solutions and decay rates to a given nonlinear hyperbolic problem.

We prove existence and asymptotic behaviour of a weak solutions of a mixed problem for $$\begin{array}{cc}& u^{\text{'}\text{'}}+Au-\Delta u^{\text{'}}+{\left|v\right|}^{\rho +2}{\left|u\right|}^{\rho }u=f_1\hfill \\ & v^{\text{'}\text{'}}+Av-\Delta v^{\text{'}}+{\left|u\right|}^{\rho +2}{\left|v\right|}^{\rho }v=f_2*\hfill \end{array}$$ where $A$ is the pseudo-Laplacian operator.