RT Journal Article
T1 Attractors of parabolic problems with nonlinear boundary conditions uniform bounds
A1 Arrieta Algarra, José María
A1 Carvalho, Alexandre N.
A1 Rodríguez Bernal, Aníbal
AB The authors study the asymptotic behavior of solutions to a semilinear parabolic problem u t −div(a(x)∇u)+c(x)u=f(x,u)  for u=u(x,t), t>0, x∈Ω⊂⊂R N , a(x)>m>0; u(x,0)=u 0   with nonlinear boundary conditions of the form u=0  on Γ 0 ,  and a(x)∂ n u+b(x)u=g(x,u)  on Γ 1  , where Γ i   are components of ∂Ω . Under smoothness and growth conditions which ensure the local classical well-posedness of the problem, they indicate some sign conditions under which the solutions are globally defined in time, and somewhat more strong dissipativeness conditions under which they possess a global attractor that captures the asymptotic dynamics of the system. After that the authors study the dependence of the attractors on the diffusion. For a(x)=a ε (x)  they show their upper semicontinuity on ε . Throughout the paper they also pay special attention to the dependence of the estimates obtained on the domain Ω  and show that in certain instances the L ∞   bounds on the attractors do not depend on the shape of Ω  but rather on |Ω| .
PB Taylor & Francis
SN 0360-5302
YR 2000
FD 2000
LK https://hdl.handle.net/20.500.14352/57904
UL https://hdl.handle.net/20.500.14352/57904
LA eng
DS Docta Complutense
RD 3 abr 2025