RT Journal Article
T1 Equilibria and global dynamics of a problem with bifurcation from infinity
A1 Arrieta Algarra, José María
A1 Pardo San Gil, Rosa María
A1 Rodríguez Bernal, Aníbal
AB We consider a parabolic equation ut−Δu+u=0 with nonlinear boundary conditions  , where  as |s|→∞. In [J.M. Arrieta, R. Pardo, A. Rodríguez-Bernal, Bifurcation and stability of equilibria with asymptotically linear boundary conditions at infinity, Proc. Roy. Soc. Edinburgh Sect. A 137 (2) (2007) 225–252] the authors proved the existence of unbounded branches of equilibria for λ close to a Steklov eigenvalue of odd multiplicity. In this work, we characterize the stability of such equilibria and analyze several features of the bifurcating branches. We also investigate several question related to the global dynamical properties of the system for different values of the parameter, including the behavior of the attractor of the system when the parameter crosses the first Steklov eigenvalue and the existence of extremal equilibria. We include Appendix A where we prove a uniform antimaximum principle and several results related to the spectral behavior when the potential at the boundary is perturbed.
PB Elsevier
SN 0022-0396
YR 2009
FD 2009
LK https://hdl.handle.net/20.500.14352/41985
UL https://hdl.handle.net/20.500.14352/41985
LA eng
DS Docta Complutense
RD 6 may 2024