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A comprehensive theory on generalized BBKS schemes
ArticleAbstract: In the past years several unconditionally positivity preserving numerical methods for production-desPalabras claves:Linear invariants, Mass conservation, Patankar-type schemes, Runge–Kutta methods, Unconditional positivityAutores:Ándres I. Ávila, Kopecz S., Meister A.Fuentes:scopusA family of new globally convergent linearization schemes for solving Richards' equation
ArticleAbstract: The Richards' equation models the water flow through porous media in groundwater aquifers and petrolPalabras claves:Degenerate nonlinear equations, Globally convergent schemes, Linearization schemes, Richards' equationAutores:Ándres I. Ávila, Guillermo AlbujaFuentes:scopusA result on singularly perturbed elliptic problems
ArticleAbstract: We consider a class of equations of the form -ε2Δu + V(x)u = f(u), u ∈ H1(RN). For a local minimum xPalabras claves:Singularly perturbed elliptic problems, Variational methodsAutores:Ándres I. Ávila, Jeanjean L.Fuentes:scopusA unified approach to symmetry for semilinear equations associated to the Laplacian in R<sup>N</sup>
ArticleAbstract: We show radial symmetry of positive solutions to the Hénon equation −Δu=|x|−ℓuq in RN∖{0}, where ℓ≥0Palabras claves:Entire solution, Maximum principle, Semi-linear elliptic equation, symmetryAutores:Ándres I. Ávila, Brock F.Fuentes:scopusAsymptotics at infinity of solutions for p-Laplace equations in exterior domains
ArticleAbstract: Let 1 < p < N, and u be a nonnegative solution of - Δp u = f (x, u) on RN {set minus} over(B1, -) whPalabras claves:Asymptotics, Entire solution, Nonlinear elliptic equation, Nonlinear System, p-LaplaceAutores:Ándres I. Ávila, Brock F.Fuentes:scopusAn adaptive Galerkin method for the time-dependent complex Schrödinger equation
ArticleAbstract: Nonlinear time-dependent Schrödinger equations (NLSE) model several important problems in quantum phPalabras claves:Adaptive Galerkin method, Dual weighted residual method, Nonlinear time-dependent Schrödinger equationAutores:Ándres I. Ávila, Meister A., Steigemann M.Fuentes:scopusAn analytic approach to maximize entropy for computing equilibrium densities of k-mers on linear chains
ArticleAbstract: The irreversible adsorption of polyatomic (or k-mers) on linear chains is related to phenomena suchPalabras claves:Blocked states, Boltzmann-Gibbs-Shannon entropy, Equilibrium density, K-mer adsorption, Linear chainsAutores:Ándres I. Ávila, González-Flores M.I., Lebrecht W.Fuentes:scopusExtension of modified Patankar–Runge–Kutta schemes to nonautonomous production–destruction systems based on Oliver's approach
ArticleAbstract: The mathematical modeling of various real life applications leads to systems of ordinary differentiaPalabras claves:Conservativity, Modified Patankar–Runge–Kutta methods, Oliver's approach, Positivity, Second orderAutores:Ándres I. Ávila, Galo Javier González, Kopecz S., Meister A.Fuentes:scopusLocating peaks of a Schrödinger equation with sign-changing nonlinearity
ArticleAbstract: In this paper, we study the concentration phenomenon of a positive ground state solution of a nonlinPalabras claves:Energy functional, Schrdinger equation, Spike solutionsAutores:Ándres I. Ávila, Yang J.Fuentes:scopusMultiscale modeling of elastic waves: Theoretical justification and numerical simulation of band gaps.
ArticleAbstract: We consider a three-dimensional composite material made of small inclusions periodically embedded inPalabras claves:Band gaps, Composite Materials, Elastic waves, homogenization, Negative mass density, Strong heterogeneitiesAutores:Ándres I. Ávila, Griso G., Miara B., Rohan E.Fuentes:scopus