RT Journal Article
T1 Pullback attractors and extremal complete trajectories for non-autonomous reaction-diffusion problems
A1 Rodríguez Bernal, Aníbal
A1 Vidal López, Alejandro
A1 Robinson, James C.
AB We analyse the dynamics of the non-autonomous nonlinear reaction–diffusion equation ut −_u = f (t,x,u),subject to appropriate boundary conditions, proving the existence of two bounding complete trajectories, one maximal and one minimal. Our main assumption is that the nonlinear term satisfies a bound of the form f (t,x,u)u _ C(t, x)|u|2 + D(t, x)|u|, where the linear evolution operator associated with _ + C(t, x) is exponentially stable. As an important step in our argument we give a detailed analysis of the exponential stability properties of the evolution operator for the non-autonomous linear problem ut − _u = C(t, x)ubetween different Lp spaces.
PB Elsevier
SN 0022-0396
YR 2007
FD 2007
LK https://hdl.handle.net/20.500.14352/49691
UL https://hdl.handle.net/20.500.14352/49691
LA eng
NO MEC
DS Docta Complutense
RD 5 may 2025