Lower semicontinuity of attactors for parabolic problems in thin domains

Author(s)

Ricardo Parreira da Silva

• Document type: Doctoral Thesis
• Press: São Carlos.
• Institution: Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB)
• Defense date: 2007-10-30

Examining board members

Alexandre Nolasco de Carvalho; Maria do Carmo Carbinatto; Milton da Costa Lopes Filho; Arnaldo Simal do Nascimento; Antonio Luiz Pereira

• Advisor: Alexandre Nolasco de Carvalho; José María Arrieta Algarra

Abstract

In this work we study semilinear reaction-diffusion problems of the type \'u IND.t(x, t) = \'DELTA\'u(x, t)+ f (u(x, t)), x \' PERTENCE A\' \'OMEGA\' \'PARTIAL\'u/\'ARTIAL\' v (x, t) = 0, x \"PERTENCE A\' \'PARTIAL\' \' OMEGA\' We develop a abstract theory to obtain the continuity of the asymptotic dynamics of (P) under singular perturbations of the spatial domain W and we apply that to many examples in thin domains (AU)