Quasilinear abstract parabolic evolution equations and exponential attractors
The authors suggest a general strategy for construction of an exponential attractor for a dynamical system determined from the quasilinear abstract parabolic evolution equation \(\frac{dU}{dt}=A(U)U=F(U)\), \(0<t<\infty\), \(U(0)=U_0\), in a Banach space \(X\). Here, \(Z\) is a Banach space continuously imbedded in \(X\), \(K\) is an open ball in \(Z\) and for each \(U\in K\) \(A(U)\) is a densely defined closed linear operator in \(X\) with the domain \(D(A(U))\) independent of \(U\in K\); \(F\) is a nonlinear operator from \(K\) into \(X\). The obtained abstract results are applied to the chemotaxis-growth system in nonsmooth domain.
scientific article; zbMATH DE number 2165815