Second order parabolic equations with non-local boundary conditions on L∞(Ω) and C(Ω̅): generation, regularity and asymptotics

Abstract

The aim of the present thesis is to analyze second order parabolic equations with non-local boundary conditions of Dirichlet and Robin type on the spaces L∞(Ω) and C(Ω̅). We will prove well-posedness of such equations and for its solutions we will prove regularity results as well as give results on the asymptotic behavior as t → ∞ . One of our main arguments is the transference of properties of the equation with local boundary conditions to the one with non-local boundary conditions. Great care will be taken to ensure that we do not need more regularity assumptions on Ω and on the coefficients of differential operator compared to the best known local results.