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oai:docta.ucm.es:20.500.14352/579042023-08-28T04:25:46Zcom_20.500.14352_14col_20.500.14352_15

Attractors of parabolic problems with nonlinear boundary conditions uniform bounds Arrieta Algarra, José María Carvalho, Alexandre N. Rodríguez Bernal, Aníbal 517.9 Semilinear equation Groth restrictions Sign conditions Dissipativeness condition Ecuaciones diferenciales 1202.07 Ecuaciones en Diferencias 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| . Depto. de Análisis Matemático y Matemática Aplicada Fac. de Ciencias Matemáticas TRUE pub 2023-06-20T17:10:58Z 2023-06-20T17:10:58Z 2000 journal article https://hdl.handle.net/20.500.14352/57904 0360-5302 10.1080/03605300008821506 eng restricted access application/pdf Taylor & Francis