Semilinear parabolic problems in thin domains with a highly oscillatory boundary

Arrieta, José M.; Carvalho, Alexandre N.; Pereira, Marcone C.; Silva, Ricardo P.

doi:10.1016/j.na.2011.05.006

Cited by 73 publications

(67 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The goal is to understand how variations of some parameters in specific models can determine the evolution of their states. For recent works in this issue, we refer the reader to [1][2][3][4][5][6] and references given there as well.…”

Section: Introductionmentioning

confidence: 99%

Perturbation of a nonautonomous problem in

Capelato

Schiabel-Silva

Silva

2013

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 99%

Perturbation of a nonautonomous problem in

Capelato

Schiabel-Silva

Silva

2013

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

“…Indeed, in [9,10,8,11,47] thin domains with highly oscillatory boundaries have been studied in a theoretical framework and convergence results have been obtained, mostly for elliptic or stationary problems. In comparison with our work we do not assume a thin domain.…”

Section: Literature Reviewmentioning

confidence: 99%

Effective rough boundary parametrization for reaction-diffusion systems

Mocenni

Sparacino

Zubelli

2014

APPL ANAL DISCRETE M

View full text Add to dashboard Cite

We address the problem of parametrizing the boundary data for reactiondiffusion partial differential equations associated to distributed systems that possess rough boundaries. The boundaries are modeled as fast oscillating periodic structures and are endowed with Neumann or Dirichlet boundary conditions. Using techniques from homogenization theory and multiple-scale analysis we derive the effective equation and boundary conditions that are satisfied by the homogenized solution. We present numerical simulations that validate our theoretical results and compare it with the alternative approach based on solving the same equation with a smoothed version of the boundary. The numerical tests show the accuracy of the homogenized solution to the effective system vis a vis the numerical solution of the original differential equation. The homogenized solution is shown undergoing dynamical regime shifts, such as anticipation of pattern formation, obtained by varying the diffusion coefficient.

show abstract

“…Associated with boundary oscillation (rough boundary) on thin structures, Arrieta et al [2] consider…”

Section: Introductionmentioning

confidence: 99%