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
Identifiers
5 results
Search Results
Now showing 1 - 5 of 5
Item Equilibria and global dynamics of a problem with bifurcation from infinity(Journal of Differential Equations, 2009) Arrieta Algarra, José María; Pardo San Gil, Rosa María; Rodríguez Bernal, AníbalWe 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.Item Infinite resonant solutions and turning points in a problem with unbounded bifurcation(International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 2010) Arrieta Algarra, José María; Pardo San Gil, Rosa María; Rodríguez Bernal, AníbalSummary: "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.''Item Asymptotic behavior of degenerate logistic equations(Journal of Differential Equations, 2015) Arrieta Algarra, José María; Pardo San Gil, Rosa María; Rodríguez Bernal, AníbalWe analyze the asymptotic behavior of positive solutions of parabolic equations with a class of degenerate logistic nonlinearities of the type lambda u - n(x)u(rho). An important characteristic of this work is that the region where the logistic term n(.) vanishes, that is K-0 ={x : n(x) = 0}, may be non-smooth. We analyze conditions on lambda, rho, n(.) and K-0 guaranteeing that the solution starting at a positive initial condition remains bounded or blows up as time goes to infinity. The asymptotic behavior may not be the same in different parts of K-0.Item Bifurcation and stability of equilibria with asymptotically linear boundary conditions at infinity(Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2007) Arrieta Algarra, José María; Pardo San Gil, Rosa María; Rodríguez Bernal, AníbalWe consider an elliptic equation with a nonlinear boundary condition which is asymptotically linear at infinity and which depends on a parameter. As the parameter crosses some critical values, there appear certain resonances in the equation producing solutions that bifurcate from infinity. We study the bifurcation branches, characterize when they are sub- or supercritical and analyse the stability type of the solutions. Furthermore, we apply these results and techniques to obtain Landesman–Lazer-type conditions guaranteeing the existence of solutions in the resonant case and to obtain an anti-maximum principleItem Localization phenomena in a degenerate logistic equation(Electronic Journal of Differential Equations, Conference 21, 2014) Arrieta Algarra, José María; Pardo San Gil, Rosa María; Rodríguez Bernal, AníbalWe analyze the behavior of positive solutions of elliptic equations with a degenerate logistic nonlinearity and Dirichlet boundary conditions. Our results concern existence and strong localization in the spatial region in which the logistic nonlinearity cancels. This type of nonlinearity has applications in the nonlinear Schrodinger equation and the study of Bose–Einstein condensates. In this context, our analysis explains the fact that the ground state presents a strong localization in the spatial region in which the nonlinearity cancels.