Ricardo P. Silva

Remarks on the p-Laplacian on thin domains

The limiting behavior of solutions of quasilinear elliptic equations on thin domains is investigated. As we will see the boundary conditions play an important role. If one considers homogeneous Dirichlet boundary conditions, the sequence of solutions will converge to the null function, whereas, if one considers Neumann boundary conditions, there is a nontrivial equation which determines the limiting behavior.

Behavior of the -Laplacian on Thin Domains

We give the characterization of the limiting behavior of solutions of elliptic equations driven by the -Laplacian operator with Neumann boundary conditions posed in a family of thin domains.

A NOTE ON RESOLVENT CONVERGENCE ON A THIN DOMAIN

In this note we combine methods presented in [1] and [3] to obtain convergence with respect to strong norms of resolvent operators associated with partial di erential equations on thin domains.

Parabolic equations in a singularly time dependent domain

We study the limiting regime of nonlinear parabolic equations posed in a time dependent family of domains { Ω e t }t € R C R n+1 which collapses to a lower dimensional set as the parameter ɛ goes to 0.

Reaction-diffusion equations in a noncylindrical thin domain

In this paper we are concerned with nonlinear reaction-diffusion equations posed in a time-dependent family of domains {Ωtϵ}t∈R⊂Rn+1 which collapses to a lower dimensional set as the parameter ϵ goes to 0.MSC:35K58, 35B41.