arXiv subjects
Publications and source records attributed to Ricardo Parreira da Silva.
We illustrate, with a simple example of domain perturbation problem, how Linear Algebra can be applied to determine the behavior of a family of partial differential equations posed in a thin rectangular domain. (In portuguese)
In this work we analyze convergence of solutions for the Laplace operator with Neumann boundary conditions in a two-dimensional highly oscillating domain which degenerates into a segment (thin domains) of the real line. We consider the case where the height of the thin domain, amplitude and period of the oscillations are all of the same order, given by a small parameter $ε$. We investigate strong convergence properties of the solutions using an appropriate corrector approach. We also give error estimates when we replace the original solutions for the second-order expansion through the Multiple-Scale Method.
In this paper we prove a stability result about the asymptotic dynamics of a perturbed nonautonomous evolution equation in $\mathbb{R}^n$ governed by a maximal monotone operator.
We consider the family of singularly nonautonomous plate equation with structural damping \[ u_{tt} + a(t,x)u_{t} + (- Δ) u_{t} + (-Δ)^{2} u + λu = f(u), \] in a bounded domain $Ω\subset \R^n$, with Navier boundary conditions. When the nonlinearity $f$ is dissipative we show that this problem is globally well posed in $H^2_0(Ω) \times L^2(Ω)$ and has a family of pullback attractors which is upper-semicontinuous under small perturbations of the damping $a$.