Person:
Pardo San Gil, Rosa María

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First Name
Rosa María
Last Name
Pardo San Gil
Affiliation
Universidad Complutense de Madrid
Faculty / Institute
Ciencias Químicas
Department
Análisis Matemático Matemática Aplicada
Area
Matemática Aplicada
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2009 - 20102
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    Publication
    Infinite resonant solutions and turning points in a problem with unbounded bifurcation
    (World Scientific Publishing, 2010) Arrieta Algarra, José María; Pardo San Gil, Rosa María; Rodríguez Bernal, Aníbal
    Summary: "We consider an elliptic equation −Δu+u=0 with nonlinear boundary conditions ∂u/∂n=λu+g(λ,x,u) , where (g(λ,x,s))/s→0 as |s|→∞ . In [Proc. Roy. Soc. Edinburgh Sect. A 137 (2007), no. 2, 225--252; MR2360769 (2009d:35194); J. Differential Equations 246 (2009), no. 5, 2055--2080; MR2494699 (2010c:35016)] the authors proved the existence of unbounded branches of solutions near a Steklov eigenvalue of odd multiplicity and, among other things, provided tools to decide whether the branch is subcritical or supercritical. In this work, we give conditions on the nonlinearity, guaranteeing the existence of a bifurcating branch which is neither subcritical nor supercritical, having an infinite number of turning points and an infinite number of resonant solutions.''
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    Publication
    Equilibria and global dynamics of a problem with bifurcation from infinity
    (Elsevier, 2009) Arrieta Algarra, José María; Pardo San Gil, Rosa María; Rodríguez Bernal, Aníbal
    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.