Lineas de Investigacion

Los temas de investigación que actualmente me interesan, se centran en el área del Análisis Numérico para la resolución de Ecuaciones en Derivadas Parciales. Me interesa particularmente el estudio de convergencia y estabilidad de los métodos numéricos (Métodos de Volúmenes Finitos, y Diferencias Finitas Conservativas), y las aplicaciones en diversas ramas de la Ingeniería y las Ciencias Físicas. Esta investigación la realizo en el contexto de mis proyectos de investigación individuales y asociativos, y físicamente en el Departamento de Ingeniería Matemática (DIM), de la Universidad de Concepción y en el Centro de Investigación en Ingeniería Matemática (CI²MA) de la misma Instiutución. Algunas de mis publicaciones divididas por temas de investigación, son las siguientes:

Problemas Inversos para leyes de Conservacion: (Click Here!)

[1] Francois James and Mauricio Sepulveda. Parameter identification for an hyperbolic equation modelling chromatography in Nonlinear Hyperbolic Problems: Theoretical, Applied and Computational Aspects. A. Donato & F. Oliveri, eds. Notes on Numerical Fluid Mechanics, Vol. 43, Vieweg, Wien, (1993) pp. 347-353. [2] Francois James and Mauricio Sepulveda. Parameter identification for a model of chromatographic column. Institute of Physics Publishing. Inverse Problems, 10, (1994) pp. 1299-1314. [3] Willy Jager, Marie Postel, Mauricio Sepulveda and Patrick Valentin. Numerische Simulation und Identifizierung reaktiver Flussigkeiten in einer Chromatographiesaule in Mathematik usseltechnologie fur die Zukunft. Verbundprojekte zwischen Universitat und Industrie. K.H. Hoffmann, W. Jager, T. Lohmann & H. Schunck, eds. Springer, Heidelberg, (1996) pp. 219-229. [4] Francois James, Mauricio Sepulveda. Convergence result for the flux identification in a scalar conservation law. SIAM Journal on Control and Optimization, Vol. 37, 3 (1999) pp. 869-891. [5] Frederic Charton, Georges Guiochon, Francois James, Igor Quinones and Mauricio Sepulveda. Determination of binary competitive equilibrium isotherms from the individual chromatographic band profiles. Chemical Engineering Sciences, 54(11), (1999), 1677--1696. [6] Georges Guiochon, Francois James and Mauricio Sepulveda. Numerical results for the flux identification in a system of conservation laws in Hyperbolic Problems: Theory, Numerics, Applications. Seventh International Conference in Zurich, February 1998, Vol I. Michael Fey & Rolf Jeltsch, eds. ISNM, Vol. 129, Birkhauser Verlag (1999), 423-432. [7] Anibal Coronel, Francois James and Mauricio Sepulveda. Numerical identification of parameters for a model of sedimentation processes. Inverse Problems, 19 (2003) pp. 951-972 [8] Stefan Berres, Raimund Burger, Anibal Coronel and Mauricio Sepulveda, Numerical identification of parameters for a strongly degenerate convection-diffusion problem modelling centrifugation of flocculated suspensions. Applied Numerical Mathematics, 52 (2005), 311-337. [9] Stefan Berres, Raimund Burger, Anibal Coronel and Mauricio Sepulveda, Numerical identification of parameters for a flocculated suspension from concentration measurements during batch centrifugation. Chemical Engineering Journal, vol. 111, 2-3 (2005), 91-103. [10] Raimund Burger, Anibal Coronel and Mauricio Sepulveda, A numerical descent method for an inverse problem of scalar conservation law modelling sedimentation. In: Numerical Mathematics and Advanced Applications, Proceedings ENUMATH 2007, K. Kunisch, G. Of and O. Steinbach (eds.), pp. 225-232, Springer Verlag, 2008.. [11] Raimund Burger, Anibal Coronel and Mauricio Sepulveda, Numerical solution of an inverse problem for a scalar conservation law modelling sedimentation. In Hyperbolic Problems: Theory, Numerics, Applications. Proceedings of Symposia in Applied Mathematics. E. Tadmor, J.-G. Liu and A.E. Tzavaras (eds). pp. 445-455, AMS, 2009.

Ecuaciones Parabolicas Fuertemente Degeneradas: (Click Here!)

[1] Raimund Burger, Alice Kozakevicius and Mauricio Sepulveda, A multiresolution finite difference scheme for spatially one-dimensional strongly degenerate parabolic equations. Scientia. Series A: Mathematical Sciences. Vol 13 (2006), 22-35. [2] Raimund Burger, Anibal Coronel and Mauricio Sepulveda, On an upwind difference scheme for strongly degenerate parabolic equations modelling the settling of suspensions in centrifuges and non-cylindrical vessels. Applied Numerical Mathematics, vol. 56, Nos. 10-11 (2006), 1397-1417. [3] Raimund Burger, Anibal Coronel and Mauricio Sepulveda, A semi-implicit monotone difference scheme for an initial- boundary value problem of a strongly degenerate parabolic equation modelling sedimentation-consolidation processes. Mathematics of Computation, vol. 75, No. 253 (2006) 91-112. [4] Raimund Burger, Alice Kozakevicius and Mauricio Sepulveda, Multiresolution schemes for strongly degenerate parabolic equations. Numerical Methods for Partial Differential Equations. Vol 23, Issue 3 (2007), 706-730. [5] Raimund Burger, Ricardo Ruiz, Kai Schneider and Mauricio Sepulveda. Multiresolution schemes for an extended clarifier-thickener model. PAMM: Proceedings in Applied Mathematics and Mechanics. Vol 7, (2007), 1041803-1041804. [6] Raimund Burger, Ricardo Ruiz, Kai Schneider and Mauricio Sepulveda, Fully adaptative multiresolution schemes for strongly degenerate parabolic equations with discontinuous flux. Journal of Engineering Mathematics. Vol 60, Issues 3-4 (2008) 365-385. [7] Raimund Burger, Ricardo Ruiz, Kai Schneider and Mauricio Sepulveda, Fully adaptive multiresolution schemes for strongly degenerate parabolic equations in one space dimension. M2AN Math. Model. Numer. Anal. Vol 42, (2008), 535-563.

Problemas de Medios Porosos: (Click Here!)

[1] Marie Postel and Mauricio Sepulveda Modelling and numerical analysis for the propagation of a fluid on a porous medium in Numerical Methods in Mechanics. C. Conca and G. Gatica, eds. Pitman Research Notes in Math Series, 371. (1997) pp. 121-130. [2] Emilio Cariaga, Fernando Concha and Mauricio Sepulveda, Flow through porous media with applications to heap leaching of copper ores. Chemical Engineering Journal, vol. 111, 2-3 (2005), 151-165. [3] Emilio Cariaga, Fernando Concha and Mauricio Sepulveda, Simultaneous modeling of liquid and gaseous phases in heap leaching for copper production. Proc. of the III International Copper Hydrometallurgy Workshop (2005), 301-315. [4] Emilio Cariaga, Fernando Concha and Mauricio Sepulveda, Flow and transport in leaching heaps: applications of the theory of multiphase flow through porous media. Proc. of the IV International Copper Hydrometallurgy Workshop, May 16-18, 2007, Vina del Mar, Chile (2007) 255-261. [5] Emilio Cariaga, Fernando Concha and Mauricio Sepulveda, Convergence of a MFE-FV method for two phase flow with applications to heap leaching of copper ores. Computer Methods in Applied Mechanics and Engineering. Vol 196, Issues 25-28 (2007) 2541-2554. [6] Iuliu S. Pop, Florin A. Radu, Mauricio Sepulveda and Octavio P. Vera Villagran, Error estimates for the finite volume discretization for the porous medium equation. Journal of Computational and Applied Mathematics. In Press. [7] Emilio Cariaga, Fernando Concha, Iuliu S. Pop and Mauricio Sepulveda, Convergence analysis of a vertex-centered finite volume scheme for a copper heap leaching model. Mathematical Methods in the Applied Sciences. In press.

Problemas Dispersivos (KdV, Schrodinger): (Click Here!)

[1] Juan Carlos Ceballos, Mauricio Sepulveda and Octavio Vera, Gain in regularity for a coupled nonlinear Schrodinger system. Boletim da Sociedade Paranaense de Matematica. Vol 24, Issue 1-2 (2006), 41-68. [2] Mauricio Sepulveda and Octavio Vera Villagran, Numerical Method for a transport equation perturbated by dispersive terms of 3rd and 5th order. Scientia. Series A: Mathematical Sciences. Vol 13 (2006), 13-21. [3] Mauricio Sepulveda, Octavio Vera Villagran and Vanilde Bisognin. Coupled system of Korteweg-de Vries equation-type in domains with oscillatory moving boundaries. PAMM: Proceedings in Applied Mathematics and Mechanics. Vol 7, (2007), 2040043-2040044. [4] Mauricio Sepulveda and Octavio Vera Villagran Numerical methods for the KdV-Kawahara and Benney-Lin equations. PAMM: Proceedings in Applied Mathematics and Mechanics. Vol 7, (2007), 2020033-2020034. [5] Juan Carlos Ceballos, Mauricio Sepulveda and Octavio Vera, The Korteweg-de Vries-Kawahara equation in a bounded domain and some numerical results. Applied Mathematics and Computation. Vol 190, (2007) 912-936. [6] Eleni Bisognin, Vanilde Bisognin, Mauricio Sepulveda and Octavio Vera, Coupled system of Korteweg de Vries equations type in domains with moving boundaries. Journal of Computational and Applied Mathematics. Vol. 220, (2008), 290-321. [7] Julie Levandovsky, Mauricio Sepulveda and Octavio Vera Villagran Gain of Regularity for the KP-I Equation. Journal of Differential Equation. Vol 245, (2008), 762-808. [8] Mauricio Sepulveda and Octavio Vera Villagran Numerical methods for a coupled nonlinear Schrodinger system. Boletin de la Sociedad Espanola de Matematica Aplicada. Vol 43, (2008), 95-102. [9] Vanilde Bisognin, Mauricio Sepulveda and Octavio Vera, On the nonexistence of asymptotically free solutions for a coupled nonlinear Schrodinger system. Applied Numerical Mathematics, Vol 59 (2009) 2285-2302. [10] Margareth Alves, Mauricio Sepulveda and Octavio Vera, Smoothing properties for the higher order nonlinear Schrodinger equation with constant coefficients. Nonlinear Analysis, TMA, Vol 71 (2009) 948-966. [11] Ademir Pazoto, Mauricio Sepulveda and Octavio P. Vera Villagran, Uniform stabilization of numerical schemes for the critical generalized Korteweg-de Vries equation with damping. Numerische Mathematik. In press.

Dinamica de Poblaciones: (Click Here!)

[1] Carlos Alberto Raposo, Mauricio Sepulveda, Octavio Vera Villagran, Ducival Carvallo Pereira and Mauro Lima Santos Solution and Asymptotic Behaviour for a Nonlocal Coupled System of Reaction-Diffusion. Acta Applicandae Mathematicae. Vol 102, Issue 1 (2008), 37-56. [2] Mostafa Bendahmane and Mauricio Sepulveda, Convergence of a finite volume scheme for nonlocal reaction-diffusion systems modelling an epidemic disease. Discrete and Continuous Dynamical Systems - Series B. Vol. 11, 4 (2009) 823-853. [3] Veronica Anaya, Mostafa Bendahmane and Mauricio Sepulveda Mathematical and numerical analysis for reaction-diffusion systems modeling the spread of early tumors. Boletin de la Sociedad Espanola de Matematica Aplicada. Vol 47, (2009), 55-62. [4] Veronica Anaya, Mostafa Bendahmane and Mauricio Sepulveda A numerical analysis of a reaction-diffusion system modelling the dynamics of growth tumors. Mathematical Models and Methods in Applied Sciences. In press. [5] Veronica Anaya, Mostafa Bendahmane and Mauricio Sepulveda Mathematical and numerical analysis for predator-prey system in a polluted environment. Networks and Heterogeneous Media. To appear.

Termoviscoelasticidad: (Click Here!)

[1] Margareth Alves, Jaime Munoz Rivera, Mauricio Sepulveda and Octavio Vera, A thermoviscoelastic system with memory in one space dimension. Relatorio de Pesquisa, 1/2009, LNCC - Petropolis/RJ . Submitted. [2] Margareth Alves, Jaime Munoz Rivera, Mauricio Sepulveda and Octavio Vera, Exponential stability in a thermoviscoelastic mixtures of solids. International Journal of Solids and Structures. Vol 46 (2009) 4151-4162. [3] Margareth Alves, Jaime Munoz Rivera, Mauricio Sepulveda and Octavio Vera, Analyticity of semigroups associated with thermoviscoelastic mixtures of solids. Journal of Thermal Stresses. Vol 32 (2009), 986-1004 [4] Margareth Alves, Carlos Alberto Raposo, Jaime Munoz Rivera, Mauricio Sepulveda and Octavio Vera, Uniform stabilization for the transmission problem of the Timoshenko system with memory. Journal of Mathematical Analysis and Applications. Vol 369 (2010), 323-345.

Otros (Homogeneizacion, Leyes de Conservacion): (Click Here!)

[1] Carlos Conca and Mauricio Sepulveda. Resultados numericos en el problema de la rejilla de Stokes. Revista Internacional de Metodos Numericos para Calculo y Diseno en Ingenieria. Universitat Politecnica de Catalunya. Espana. Vol. 5, 4, (1989) pp. 435-452. [2] Francois James, Mauricio Sepulveda and Patrick Valentin. Statistical thermodynamics models for a multicomponent two-phases equilibrium isotherm. Maths. Models and Methods in Applied Science, 7(1), (1997) pp. 1-29. [3] Francois James, Marie Postel and Mauricio Sepulveda. Numerical comparison between relaxation and nonlinear equilibrium models. Application to chemical engineering. Physica D, Vol 138, 3-4 (2000) pp. 316-333. [4] Yunguang Lu and Mauricio Sepulveda. Artificial and physical viscosity solutions for a hyperbolic conservation system. Applicable Analysis, Vol. 78(1-2), 2001, pp. 33-43. [5] Francisco Caicedo, Yunguang Lu and Mauricio Sepulveda. Relaxation approximations and BV estimates for some partial differential equations. Electron. J. Diff. Eqns. , Vol. 2002(2002), No. 19, pp. 1-10.