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Existence and Long-Time Behavior of Variational Solutions to a Class of Nonclassical Diffusion Equations in Noncylindrical Domains
Nguyen Duong Toan

 

Abstract

We prove the existence and uniqueness of variational solutions to the following non-autonomous nonclassical diffusion equation
utΔutΔu+f(u)=g(x,t)
in a noncylindrical domain with the homogeneous Dirichlet boundary condition, under assumptions that the spatial domains are bounded and increase with time, the nonlinearity f satisfies growth and dissipativity conditions of Sobolev type, and the external force g is time-dependent. Moreover, the nonautonomous dynamical system generated by this class of solutions is shown to have a pullback attractor A^={A(t):tR} .
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