|
Resumen:
|
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????R N , a(x)>m>0; u(x,0)=u 0 with nonlinear boundary conditions of the form u=0 on ? 0 , and a(x)? n u+b(x)u=g(x,u) on ? 1 , where ? i are components of ?? . 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 ? (x) they show their upper semicontinuity on ? . Throughout the paper they also pay special attention to the dependence of the estimates obtained on the domain ? and show that in certain instances the L ? bounds on the attractors do not depend on the shape of ? but rather on |?| .
|
