26 research outputs found
Semilinear elliptic equations in thin regions with terms concentrating on oscillatory boundaries
In this work we study the behavior of a family of solutions of a semilinear
elliptic equation, with homogeneous Neumann boundary condition, posed in a
two-dimensional oscillating thin region with reaction terms concentrated in a
neighborhood of the oscillatory boundary. Our main result is concerned with the
upper and lower semicontinuity of the set of solutions. We show that the
solutions of our perturbed equation can be approximated with ones of a
one-dimensional equation, which also captures the effects of all relevant
physical processes that take place in the original problem
A nonlinear elliptic problem with terms concentrating in the boundary
In this paper we investigate the behavior of a family of steady state
solutions of a nonlinear reaction diffusion equation when some reaction and
potential terms are concentrated in a -neighborhood of a portion
of the boundary. We assume that this -neighborhood shrinks
to as the small parameter goes to zero. Also, we suppose
the upper boundary of this -strip presents a highly oscillatory
behavior. Our main goal here is to show that this family of solutions converges
to the solutions of a limit problem, a nonlinear elliptic equation that
captures the oscillatory behavior. Indeed, the reaction term and concentrating
potential are transformed into a flux condition and a potential on ,
which depends on the oscillating neighborhood
[Book of abstracts]
USPFAPESPCAPESICMC Summer Meeting on Differential Equations (2015 São Carlos
Book of Abstracts
USPCAPESFAPESPCNPqINCTMatICMC Summer Meeting on Differentail Equations.\ud
São Carlos, Brasil. 3-7 february 2014