Produção Nacional
Revisado por pares
Phase transition of a heat equation with Robin’s boundary conditions and exclusion process
2014; American Mathematical Society; Volume: 367; Issue: 9 Linguagem: Inglês
10.1090/s0002-9947-2014-06260-0
ISSN1088-6850
AutoresTertuliano Franco, Patrícia Gonçalves, Adriana Neumann,
Tópico(s)Advanced Mathematical Modeling in Engineering
ResumoFor a heat equation with Robin's boundary conditions which depends on a parameter $\alpha >0$, we prove that its unique weak solution $\rho ^\alpha$ converges, when $\alpha$ goes to zero or to infinity, to the unique weak solution of the heat equation with Neumann's boundary conditions or the heat equation with periodic boundary conditions, respectively. To this end, we use uniform bounds on a Sobolev norm of $\rho ^\alpha$ obtained from the hydrodynamic limit of the symmetric slowed exclusion process, plus a careful analysis of boundary terms.
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