1996-1998 Department of Mathematics, Brigham Young University, postdoctoral associate
1998-1999 Department of Mathematics and Statistics, Utah State University, visiting assistant professor
1999-2000 Department of Mathematics, Brigham Young University, postdoctoral associate
11/2000-11/2002 Department of Mathematics, Heriot-Watt University, EU Marie Curie Postdoctoral Fellow
01/2003-05/2003 Department of Mathematics and Statistics, Memorial University of Newfoundland, visiting postdoctoral associate
01/2004-08/2004 Department of Mathematics, Michigan State University, visiting assistant professor
10/2005-09/2009 Division of Integral Equations, Faculty of Mathematics and Information Science, Warsaw University of Technology, assistant professor
1991-95 Graduate, Department of Mathematics, University of Utah
E-mail: chmaj at math dot utah dot edu
Traveling waves in multicomponent reaction-diffusion systems: existence, uniqueness and stability, Ph.D. Thesis, University of Utah, August 1995.
Homoclinic solutions of an integral equation: existence and stability (with X. Ren), Journal of Differential Equations, 155 (1999), 17-43. This paper was accepted for publication in the Transactions of the AMS.
An integrodifferential model for phase transitions: stationary solutions in higher space dimensions (with P.W. Bates), Journal of Statistical Physics, 95 (1999), 1119-1139.
A discrete convolution model for phase transitions (with P.W. Bates), Archive for Rational Mechanics and Analysis, 150 (1999), 281-305.
Multiple layered solutions of the nonlocal bistable equation (with X. Ren), Physica D, 147 (2000), 135-154.
Pattern formation in the nonlocal bistable equation (with X. Ren), Methods and Applications of Analysis, 8 (2001), 369-386.
The nonlocal bistable equation: stationary solutions on a bounded interval (with X. Ren), Electronic Journal of Differential Equations, 2002(2002), No.2, 1-12.
Traveling waves of bistable dynamics on a lattice (with P.W. Bates and Xinfu Chen), SIAM Journal on Mathematical Analysis, 35 (2003), 520-546.
Equilibria and traveling waves for bistable equations with non-local and discrete dissipation (with P.W. Bates and Xinfu Chen), Kyoto Univ., Research Institute for Mathematical Sciences, No. 1178 (2000), 48-71.
Uniqueness of travelling waves for nonlocal monostable equations (with J. Carr), Proceedings of the AMS, 132 (2004), 2433-2439.
Soliton-stripe patterns of a functional with an attractive-repulsive-attractive interaction (with X. Ren), Journal of Dynamics and Differential Equations, 16 (2004), 463-476.
Heteroclinic solutions of a van der Waals model with indefinite nonlocal interactions (with P.W. Bates and Xinfu Chen), Calculus of Variations and PDEs, 24 (2005), 261-281.
Existence of traveling waves for the nonlocal Burgers equation, Applied Mathematics Letters, 20 (2007), 439-444.
Periodic microstructure: local minimizers with discontinuous interfaces in the van der Waals' nonlocal free energy phase transition model, in preparation.
Professional service: Refereed articles for: Contemporary Mathematics, Applied Mathematics Letters, Proceedings of the Royal Society of Edinburgh Sect. A, Journal of Statistical Physics, Transactions of the AMS.
Organizer of a minisymposium (Nonlocal Equations: Theory and Applications) at the SIAM Pacific Rim Dynamical Systems Conference (August 2000, Hawaii, USA).
Invited participant in the ``Defects and their dynamics'' work shop (09.08-16.08.2003) at the Banff International Research Station.
Poster presenter in the ``Workshop on Singularities in PDE and the Calculus of Variations'' (17.07.-21.07.2006) at the Centre de Recherches Mathematiques, Universite de Montreal.
G. Alberti and G. Bellettini, A non-local anisotropic model for phase transitions: asymptotic behavior of rescaled energies, Eur. J. Appl. Math., 9 (1998), 261-284.
N.D. Alikakos, P.W. Bates and X. Chen, Convergence of the Cahn-Hilliard equation to the Hele-Shaw model, Arch. Rational Mech. Anal., 128 (1994), 165-205.
C. Atkinson and G.E.H. Reuter, Deterministic epidemic waves, Math. Proc. Camb. Phil. Soc., 80 (1976), 315-330.
P.W. Bates, P.C. Fife, X. Ren and X. Wang, Traveling waves in a convolution model for phase transitions, Arch. Rational Mech. Anal., 138 (1997), 105-136.
P.W. Bates and X. Ren, Heteroclinic orbits for a higher order phase transition problems, Eur. J. Appl. Math., 8 (1997), 149-163.
J.B. van den Berg, J. Hulshof and R. van der Vorst, Travelling waves for fourth-order semilinear parabolic equations (1999), SIAM J. Math. Anal., 32 (2001), 1342-1374.
F. Bethuel, H. Brezis and F. Helein, Ginzburg-Landau vortices, Birkhauser 1994.
L. Bronsard and F. Reitich, On three-phase boundary motion and the singular limit of a vector-valued Ginzburg-Landau equation, Arch. Rational Mech. Anal., 124 (1993), 355-379.
J. Carr and R. Pego, Invariant manifolds for metastable patterns in u_t=e^2 u_{xx}-f(u), Comm. Pure Appl. Math., 42 (1989), 523-576.
R.G. Casten and C.J. Holland, Instability results for reaction diffusion equations with Neumann boundary conditions, J. Differential Equations, 27 (1978), 266-273.
X. Chen, The Hele-Shaw problem and area-preserving curve-shortening motions, Arch. Rational Mech. Anal. 123 (1993), 117-151.
X. Chen, S.-C. Fu and J.-S. Guo, Uniqueness and asymptotics of traveling waves of monostable dynamics on lattices, SIAM J. Math. Anal. 38 (2006), 233-258.
X. Chen and R. Illner, Finite-range repulsive systems of finitely many particles, Arch. Rational Mech. Anal. 173 (2004), 1-24.
X. Chen and Y. Oshita, An application of the modular function in nonlocal variational problems, Arch. Rational Mech. Anal., 186 (2007), 109-132.
R. Choksi and P. Sternberg, On the first and second variations of a nonlocal isoperimetric problem, preprint.
S. Conti, I. Fonseca and G. Leoni, A Gamma-convergence result for the two-gradient theory of phase transitions, Comm. Pure Appl. Math., 55 (2002), 857-936.
B. Deng, The existence of infinitely many traveling front and back waves in the FitzHugh-Nagumo equations, SIAM J. Math. Anal., 22 (1991), 1631-1650.
G.B. Ermentrout and J.B. McLeod, Existence and uniqueness of travelling waves for a neural network, Proc. Roy. Soc. Edinburgh Sect. A, 123 (1993), 461-478.
P.C. Fife and J.B. McLeod, The approach of solutions of nonlinear diffusion equations to travelling front solutions, Archive for Rational Mechanics and Analysis, 65 (1977), 335-361.
G. Friesecke and J.A.D. Wattis, Existence theorem for solitary waves on lattices, Commun. Math. Phys., 161 (1994), 391-418.
G. Fusco and J.K. Hale, Slow motion manifolds, dormant instability and singular perturbations, J. Dynam. Differential Equations, 1 (1989), 75-94.
N. Ghoussoub and C. Gui, On a conjecture of De Giorgi and some related problems, Math. Ann., 311 (1998), 481-491.
B. Gidas, W.-M. Ni and L. Nirenberg, Symmetry and related properties via the maximum principle, Commun. Math. Phys., 68 (1979), 209-243.
M. Grinfeld and A. Novick-Cohen, Counting stationary solutions of the Cahn-Hilliard equation by transversality arguments, Proc. Roy. Soc. Edinburgh Sect. A, 125 (1995), 351-370.
D. Henry, Geometric Theory of Semilinear Parabolic Equations, Springer Lecture Notes in Mathematics, Vol. 840 (1981).
R. Kohn and P. Sternberg, Local minimizers and singular perturbations, Proc. Roy. Soc. Edinburgh Sect. A, 111 (1989), 69-84.
H. Matano, Asymptotic behavior and stability of solutions of semilinear diffusion equations, Publ. Res. Inst. Math. Sci., Kyoto Univ., 15 (1979), 401-454.
V.J. Mizel, L.A. Peletier and W.C. Troy, Periodic phases in second-order materials, Arch. Rational Mech. Anal. 145 (1998), 343-382.
L. Modica, The gradient theory of phase transitions and the minimal interface criterion, Arch. Rational Mech. Anal., 98 (1987), 123-142.
S. Muller, Singular perturbations as a selection criterion for periodic minimizing sequences, Cal. Var. Partial Diff. Eqn., 1 (1993), 169-204.
X. Ren and L. Truskinovsky, Finite scale microstructures in 1-D elasticity, Journal of Elasticity, 59 (2000), 319-355.
X. Ren and J. Wei, On energy minimizers of the di-block copolymer problem, Interfaces and Free Boundaries, 5 (2003), 193-238.
X. Ren and J. Wei, On the spectra of 3-D lamellar solutions of the diblock copolymer problem, SIAM J. Math. Anal., 35 (2003), 1-32.
X. Ren and J. Wei, Wriggled lamellar solutions and their stability in the diblock copolymer problem, SIAM J. Math. Anal., 37 (2005), 455-489.
E. Sandier and S. Serfaty, Vortices in the Magnetic Ginzburg-Landau model, to appear.
O. Savin, Phase transitions: regularity of flat level sets, Annals of Mathematics.
D. Smets and M. Willem, Solitary waves with prescribed speed on infinite lattices, J. Functional Analysis, 149 (1997), 266-275.
J. Smoller and A. Wasserman, Global bifurcation of steady state solutions, J. Differential Equations, 39 (1981), 269-290.
J. Su, On the existence of finger solutions of the Hele-Shaw equation, Nonlinearity, 14 (2001), 153-166.
E. Yanagida, Stability of the fast travelling wave solutions of the FitzHugh-Nagumo equations, J. Math. Biol., 22 (1985), 81-104.
J.D. van der Waals, The thermodynamic theory of capillarity under the hypothesis of a continuous variation of density, translation from Dutch by J.S. Rowlingson, J. Statist. Phys., 20 (1979), 197-244.
B. Zinner, Existence of traveling wavefront solutions for the discrete Nagumo equation, Journal of Differential Equations, 11 (1992), 1-27.