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Michal Kowalczyk

Professor Titular

Universidad de Chile

Santiago, Chile

Semilinear Partial Differential Equations, Geometric Analysis, Dispersive Partial Differential Equations

Mathematics, University Of Tennessee-Knoxville. Estados Unidos, 1995

Research Assistant Professor Full Time

University of Minnesota, Minneapolis

Minneapolis, MN, Estados Unidos

1995 - 1997
Postdoctoral Researcher Full Time

Carnegie Mellon University

Pittsburgh, PA, Estados Unidos

1997 - 2000
Assistant Professor Full Time

Kent State University

Kent, OH, Estados Unidos

2001 - 2003
Associate Professor Full Time

Kent State University

Kent, OH, Chile

2003 - 2004
Profesor Asociado Full Time

Universidad de Chile

Ciencias Físicas y Matemáticas

Santiago, Chile

2004 - 2009
Profesor Titular Full Time

Universidad de Chile

Ciencias Físicas y Matemáticas

Santiago, Chile

2009 - A la fecha

Guidance of postdoctoral research:
Dr. Christos Sourdis, Title of research: “Singularities arising in a class of nonlinear problems”, (FONDECYT Postdoc 2008-2010).
Dr. Yong Liu, Title of research: “ Saddle family interface in the gradient theory of phase transitions”, (FONDECYT Postdoc 2009-2011).
Dr. Panayotis Smyrnelis, Title of research: "Minimal solutions to nonlinear systems of elliptic equations" (FONDECYT Postdoc 2015-2018)
Dr. Matteo Rizzi, Title of research: "Elliptic PDEs: qualitative properties of solutions and existence results: (FONDECYT Postdoc 2017-2019)

Current Ph.D in Mathematics: Álvaro Hernández.


Maximal solution of the Liouville equation in doubly connected domains Kowalczyk, Michal; Pistoia, Angela Article ISI SCOPUS JOURNAL OF FUNCTIONAL ANALYSIS (2019)
Nondegeneracy and the Jacobi Fields of Rotationally Symmetric Solutions to the Cahn-Hillard Equation Hernandez, Alvaro; Kowalczyk, Michal Article ISI SCOPUS INDIANA UNIVERSITY MATHEMATICS JOURNAL (2019)
On the origin of the optical vortex lattices in a nematic liquid crystal light valve Calisto, Enrique; Clerc, Marcel G.; Kowalczyk, Michal Article ISI SCOPUS OPTICS LETTERS (2019)
Symmetry Breaking and Restoration in the Ginzburg-Landau Model of Nematic Liquid Crystals Clerc, MG Article ISI SCOPUS JOURNAL OF NONLINEAR SCIENCE (2018)
KINK DYNAMICS IN THE phi(4) MODEL: ASYMPTOTIC STABILITY FOR ODD PERTURBATIONS IN THE ENERGY SPACE Kowalczyk, Micha?; Martel, Yvan Article ISI SCOPUS JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY (2017)
Nonexistence of small, odd breathers for a class of nonlinear wave equations Kowalczyk, Micha?; Martel, Yvan Article ISI SCOPUS LETTERS IN MATHEMATICAL PHYSICS (2017)
ROTATIONALLY SYMMETRIC SOLUTIONS TO THE CAHN-HILLIARD EQUATION Article ISI SCOPUS DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS (2017)
Theory of light-matter interaction in nematic liquid crystals and the second Painleve equation Kowalczyk, Micha?; Smyrnelis, Panayotis Article ISI SCOPUS CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS (2017)
Light-matter interaction induces a shadow vortex R. Barboza, U. Bortolozzo, M. G. Clerc, J. D. Davila, M. Kowalczyk, S. Residori, and E. Vidal-Henriquez Article Phys. Rev. E (2016)
A HYBRID VARIATIONAL PRINCIPLE FOR THE KELLER-SEGEL SYSTEM IN R-2 Blanchet A; Carrillo, JA; Kinderlehrer D; Kowalczyk M; Laurencot, P; Lisini, S Article ESAIM: Mathematical Modelling and Numerical Analysis (2015)
End-to-end construction for the Allen-Cahn equation in the plane Kowalczyk, M; Liu, Y; Pacard, F; Wei, JC Article CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS (2015)
Singly Periodic Solutions of the Allen-Cahn Equation and the Toda Lattice Kowalczyk, M; Liu, Y; Wei J. Article COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS (2015)
Singly Periodic Solutions of the Allen-Cahn Equation and the Toda Lattice Kowalczyk M.; Liu Y.; Wei J. Article ISI SCOPUS COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS (2015)
Transversal Instability for the Thermodiffusive Reaction-Diffusion System Kowalczyk M.; Perthame, B; Vauchelet, N Article ISI SCOPUS Chinese Annals of Mathematics. Series B (2015)
Improved interpolation inequalities on the sphere Dolbeault, Jean; Esteban, María; Kowalczyk, Michal; Loss, Michael Article ISI Discrete Continuous Dynamical System Ser. S (2014)
ENTIRE SOLUTIONS OF THE ALLEN-CAHN EQUATION AND COMPLETE EMBEDDED MINIMAL SURFACES OF FINITE TOTAL CURVATURE IN R-3 del Pino, Manuel; Kowalczyk, Michal; Wei, Juncheng Article ISI JOURNAL OF DIFFERENTIAL GEOMETRY (2013)
MODULI SPACE THEORY FOR THE ALLEN-CAHN EQUATION IN THE PLANE del Pino, M; Kowalczyk, M; Pacard, F Article TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY (2013)
Sharp Interpolation Inequalities on the Sphere: New Methods and Consequences Dolbeault, J; Esteban, MJ; Kowalczyk, M; Loss, M Article CHINESE ANNALS OF MATHEMATICS SERIES B (2013)
THE CLASSIFICATION OF FOUR-END SOLUTIONS TO THE ALLEN-CAHN EQUATION ON THE PLANE Kowalczyk, Michal; Liu, Yong; Pacard, Frank Article ANALYSIS & PDE (2013)
Traveling Waves with Multiple and Nonconvex Fronts for a Bistable Semilinear Parabolic Equation Del Pino M.; Kowalczyk M.; Wei, JC Article ISI SCOPUS Communications on Pure and Applied Mathematics (2013)
On De Giorgi's conjecture and beyond Del Pino M.; Kowalczyk M.; Wei J. Article ISI SCOPUS Proceedings of the National Academy of Sciences of the United States of America (2012)
The space of 4-ended solutions to the Allen-Cahn equation in the plane Kowalczyk M.; Liu Y.; Pacard F. Article ISI SCOPUS Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire (2012)
TOWARDS CLASSIFICATION OF MULTIPLE-END SOLUTIONS TO THE ALLEN-CAHN EQUATION IN R-2 Kowalczyk, Michal; Liu, Yong; Pacard, Frank Article ISI SCOPUS Networks and Heterogeneous Media (2012)
NONDEGENERACY OF THE SADDLE SOLUTION OF THE ALLEN-CAHN EQUATION Kowalczyk M.; Liu Y. Article ISI PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY (2011)
On De Giorgi's conjecture in dimension N >= 9 Del Pino M.; Kowalczyk M.; Wei, JC Article ISI SCOPUS Annals of Mathematics (2011)
INTERFACE FOLIATION NEAR MINIMAL SUBMANIFOLDS IN RIEMANNIAN MANIFOLDS WITH POSITIVE RICCI CURVATURE Del Pino M.; Kowalczyk M.; Wei, JC; Yang, J. Article ISI SCOPUS Geometric and Functional Analysis (2010)
Multiple-end solutions to the Allen-Cahn equation in R-2 Del Pino M.; Kowalczyk M.; Pacard F.; Wei, JC Article ISI SCOPUS Journal of Functional Analysis (2010)
THE JACOBI-TODA SYSTEM AND FOLIATED INTERFACES Del Pino M.; Kowalczyk M.; Wei, JC Article ISI SCOPUS Discrete and Continuous Dynamical Systems- Series A (2010)
The Toda system and multiple-end solutions of autonomous planar elliptic problems Del Pino M.; Kowalczyk M.; Pacard F.; Wei, JC Article ISI SCOPUS Advances in Mathematics (2010)
ENTIRE SOLUTIONS OF THE ALLEN-CAHN EQUATION AND COMPLETE EMBEDDED MINIMAL SURFACES Del Pino M.; Kowalczyk M.; Wei, JC Article ISI REVISTA DE LA UNION MATEMATICA ARGENTINA (2009)
STOCHASTIC STOKES' DRIFT, HOMOGENIZED FUNCTIONAL INEQUALITIES, AND LARGE TIME BEHAVIOR OF BROWNIAN RATCHETS Blanchet A; Dolbeault J.; Kowalczyk M. Article ISI SCOPUS SIAM JOURNAL ON MATHEMATICAL ANALYSIS (2009)
THE JANOSSY EFFECT AND HYBRID VARIATIONAL PRINCIPLES Kinderlehrer D; Kowalczyk M. Article ISI SCOPUS DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B (2009)
A counterexample to a conjecture by De Giorgi in large dimensions Del Pino M.; Kowalczyk M.; Wei, JC Article ISI SCOPUS COMPTES RENDUS MATHEMATIQUE (2008)
Critical points of the regular part of the harmonic Green function with Robin boundary condition Dávila J.; Kowalczyk M.; Montenegro M. Article ISI SCOPUS JOURNAL OF FUNCTIONAL ANALYSIS (2008)
Renormalized energy of interacting Ginzburg-Landau vortex filaments Del Pino M.; Kowalczyk M. Article ISI SCOPUS JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES (2008)
The Toda system and clustering interfaces in the Allen-Cahn equation Del Pino M.; Kowalczyk M.; Wei, JC Article ISI SCOPUS ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS (2008)
Travelling fronts in stochastic Stokes' drifts Blanchet A; Dolbeault J.; Kowalczyk M. Article ISI SCOPUS PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS (2008)
A qualitative study of linear drift-diffusion equations with time-dependent or degenerate coefficients Bartier, JP; Dolbeault J.; Illner, R; Kowalczyk M. Article ISI SCOPUS MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES (2007)
Concentration on curves for nonlinear Schrodinger equations Del Pino M.; Kowalczyk M.; Wei, JC Article ISI SCOPUS COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS (2007)
Resonance and interior layers in an inhomogeneous phase transition model Del Pino M.; Kowalczyk M.; Wei, JC Article SCOPUS SIAM JOURNAL ON MATHEMATICAL ANALYSIS (2006)
Variational reduction for Ginzburg-Landau vortices Del Pino M.; Kowalczyk M.; Musso, M Article ISI SCOPUS JOURNAL OF FUNCTIONAL ANALYSIS (2006)
Nonlinear Schrodinger equations: concentration on weighted geodesics in the semi-classical limit Del Pino M.; Kowalczyk M.; Wei, JC Article ISI SCOPUS COMPTES RENDUS MATHEMATIQUE (2005)
On the existence and Morse index of solutions to the Allen-Cahn equation in two dimensions Kowalczyk, Michal Article ISI Ann. Mat. Pura Appl. (2005)
Singular limits in Liouville-type equations Del Pino M.; Kowalczyk M.; Musso, M Article ISI SCOPUS CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS (2005)
Approximate invariant manifold of the Allen-Cahn flow in two dimensions Kowalczyk, Michal Article SCOPUS Contemporary MAthematics (2004)
Minimality and nondegeneracy of degree-one Ginzburg-Landau vortex as a Hardy's type inequality Del Pino M.; Felmer P.; Kowalczyk M. Article ISI SCOPUS INTERNATIONAL MATHEMATICS RESEARCH NOTICES (2004)
Remarks about the flashing ratchet Dolbeault, Jean; Kinderlehrer, David; Kowalczyk, Michal Article SCOPUS Contemporary MAthematics (2004)
A Variational Principle for Molecular Motors Chipot, Michel; Kinderlehrer, David; Kowalczyk, Michal Article ISI MECCANICA (2003)
Multi-bump ground states of the Gierer-Meinhardt system in R-2 Del Pino M.; Kowalczyk M.; Wei, JC Article ISI SCOPUS ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE (2003)
Boundary spikes in the Gierer-Meinhardt system Del Pino M.; Felmer P.; Kowalczyk M. Article ISI COMMUNICATIONS ON PURE AND APPLIED ANALYSIS (2002)
Diffusion mediated transport and the flushing ratchet Kinderlehrer, David; Kowalczyk, Michal Article ISI Archive Rational Mech. Analysis (2002)
Discrete and continuous ratchets: from coin toss to molecular motor Heath, David; Kinderlehrer, David; Kowalczyk, Michal Article ISI DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS (2002)
Dynamics of an interior spike in the Gierer-Meinhardt system Chen, Xinfu; Kowalczyk, Michal Article ISI SIAM Journal of Mathematical Analysis (2001)
Slow dynamics of interior spikes in the shadow Gierer-Meinhardt system Chen, Xinfu; Kowalczyk, Michal Article SCOPUS ADVANCES IN DIFFERENTIAL EQUATIONS (2001)
The Gierer & Meinhardt system: The breaking of homoclinics and multi-bump ground states Del Pino M.; Kowalczyk M.; Chen, XF Article ISI SCOPUS COMMUNICATIONS IN CONTEMPORARY MATHEMATICS (2001)
Remarks about the diffusion mediated transport Kinderlehrer, David; Kowalczyk, Michal Article ISI Ricerche Mat. (2000)
A class of pattern forming models Fife, Paul; Kowalczyk, Michal Article ISI JOURNAL OF NONLINEAR SCIENCE (1999)
Critical points of a singular perturbation problem via reduced energy and local linking Alikakos, Nicolas; Kowalczyk, Michal Article ISI JOURNAL OF DIFFERENTIAL EQUATIONS (1999)
Multiple spike layers in the shadow Gierer-Meinhardt system: existence of equilibria and approximate invariant manifold Kowalczyk, Michal Article ISI Duka Math Journal (1999)
Exponentially slow dynamics and interfaces intersecting the boundary Kowalczyk, Michal Article ISI JOURNAL OF DIFFERENTIAL EQUATIONS (1997)
Existence of equilibria for the Cahn-Hilliard equation via local minimizers of the perimeter Chen, Xinfu; Kowalczyk, Michal Article ISI Communications in PDEs (1996)
Finite dimensional dynamics and interfaces intersecting boundary Alikakos, Nicolas; Fusco, Gorgio; Kowalczyk, Michal Article ISI Indiana University Math Journal (1996)


On a conjecture by De Giorgi in dimensions 9 and higher Del Pino M.; Kowalczyk M.; Wei, JC ConferencePaper DYNAMICS AND NUMBERS (2010)


ASYMPTOTIC STABILITY OF THE VACUUM STATES AND KINKS IN A HIERARCHY OF DEFOCUSING NONLINEAR WAVE EQUATIONS MICHAL KOWALCZYK Proyecto (2017)
GEOMETRIC APPROACH TO THE THEORY OF ENTIRE SOLUTIONS TO THE ALLEN-CAHN AND GINZBURG-LANDAU EQUATIONS MICHAL KOWALCZYK Proyecto (2013)
EXISTENCE AND QUALITATIVE ANALISIS OF SOLUTIONS OF ELLIPTIC AND PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS MICHAL KOWALCZYK Proyecto (2009)
EXISTENCE, STABILITY AND DYNAMICS IN SINGULAR PERTURBATION AND MOLECULAR LEVEL TRANSPORT PROBLEMS MICHAL KOWALCZYK Proyecto (2005)