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Rodríguez Bernal, Aníbal ; Vidal López, Alejandro ; Langa, J.A. ; Robinson, James C. ; Suárez, A. | American Institute of Mathematical Sciences | 2007The goal of this work is to study the forward dynamics of positive solutions for the nonautonomous logistic equation ut ? _u = _u ? b(t)up, with p > 1, b(t) > 0, for all t 2 R, limt!1 b(t) = 0. While the pullback asymptotic behaviour for this [...]texto impreso
Rodríguez Bernal, Aníbal ; Vidal López, Alejandro | American Institute of Mathematical Sciences | 2007We give conditions for the existence of a unique positive complete trajectories for non-autonomous reaction-diffusion equations. Also, attraction properties of the unique complete trajectory is obtained in a pullback sense and also forward in ti[...]texto impreso
The authors find a growth condition on the nonlinear term f(x, u) of a nonlinear heat equation which ensures the existence of maximal and minimal equilibria that bound asymptotically all solutions to that nonlinear heat equation.texto impreso
We show the existence of two special equilibria, the extremal ones, for a wide class of reaction–diffusion equations in bounded domains with several boundary conditions, including non-linear ones. They give bounds for the asymptotic dynamics and[...]texto impreso
It is known that any periodic orbit of a Lipschitz ordinary differential equation must have period at least 2?/L, where L is the Lipschitz constant of f. In this paper, we prove a similar result for the semilinear evolution equation du/dt=-Au+f[...]texto impreso
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 mai[...]texto impreso
In this paper we show that dissipative reaction-diffusion equations in unbounded domains posses extremal semistable ground states equilibria, which bound asymptotically the global dynamics. Uniqueness of such positive ground state and their appr[...]texto impreso
En la segunda parte, se estudian problemas no autónomos. Ahora, las soluciones extremales son trayectorias completas (soluciones definidas para todo tiempo) y el concepto de atracción considerado es el de atracción pullback: lo importante es el [...]
