Xiaofeng Ren's publications and preprints

  • X. Ren and J. Wei, The spectrum of the torus profile to a geometric variational problem with long range interaction, Physica D, Vol. 351-352 (2017) 62-88.

  • X. Ren and C. Wang, A stationary core-shell assembly in a ternary inhibitory system, Discrete and Continuous Dynamical Systems - Series A, Vol. 37, No 2 (2017) 983-1012.

  • X. Ren and D. Shoup, The impact of the domain boundary on an inhibitory system: existence and location of a stationary half disc, Communications in Mathematical Physics, Vol. 340, No. 1 (2015) 355-412.

  • X. Ren and J. Wei, A double bubble assembly as a new phase of a ternary inhibitory system, Archive for Rational Mechanics and Analysis, Vol. 215, No. 3 (2015) 967-1034.

  • X. Ren and J. Wei, Asymmetric and symmetric double bubbles in a ternary inhibitory system, SIAM Journal on Mathematical Analysis, Vol. 46, No. 4 (2014), 2798-2852.

  • X. Ren and J. Wei, Double tori solution to an equation of mean curvature and Newtonian potential, Calculus of Variations and Partial Differential Equations, Vol. 49, No. 3 (2014), 987-1018.

  • X. Ren and J. Wei, A double bubble in a ternary system with inhibitory long range interaction, Archive for Rational Mechanics and Analysis, Vol. 208, No. 1 (2013), 201-253.

  • S. Gillmor, J. Lee, and X. Ren, The role of Gauss curvature in a membrane phase separation problem, Physica D, Vol 240, No. 24 (2011), 1913-1927.

  • T. Kolokolnikov and X. Ren, Smoke-ring solutions of Gierer-Meinhardt system in $R^3$, SIAM Journal on Applied Dynamical Systems, Vol. 10, No. 1 (2011), 251-277.

  • X. Ren and J. Wei, A toroidal tube solution to a problem involving mean curvature and Newtonian potential, Interfaces and Free Boundaries, Vol. 13, No. 1 (2011), 127-154.

  • X. Kang and X. Ren, The pattern of multiple rings from morphogenesis in development, Journal of Nonlinear Science, Vol. 20, No. 6 (2010), 747-779.

  • X. Ren and J. Wei, Oval shaped droplet solutions in the saturation process of some pattern formation problems, SIAM Journal on Applied Mathematics, Vol 70, No 4 (2009), 1120-1138.

  • X. Ren and J. Wei, On a phase field problem driven by interface area and interface curvature, European Journal of Applied Mathematics, Vol 20, No 6 (2009), 531-556.

  • X. Ren, Shell structure as solution to a free boundary problem from block copolymer morphology, Discrete and Continuous Dynamical Systems - Series A, Vol 24, No. 3 (2009), 979-1003.

  • X. Kang and X. Ren, Ring pattern solutions of a free boundary problem in diblock copolymer morphology, Physica D, Vol 238, No. 6 (2009), 645-665.

  • X. Ren, An Allen-Cahn type problem with curvature modification, CRM Proceedings and Lecture Notes, Singularities in PDE and Calculus of Variations, Edited by S. Alama, L. Bronsard and P. Sternberg, AMS and CRM, 2008.

  • X. Ren and J. Wei, The critical mass constraint in the Cahn-Hilliard problem, Interfaces and Free Boundaries, Vol. 10, No. 3 (2008), 301-338.

  • M. Helmers, B. Niethammer and X. Ren, Evolution in off-critical diblock copolymer melts, Networks and Heterogeneous Media, Vol 3, No. 3 (2008), 615-632.

  • X. Ren and J. Wei, Spherical solutions to a nonlocal free boundary problem from diblock copolymer morphology, SIAM Journal on Mathematical Analysis, Vol. 39, No. 5 (2008), 1497-1535.

  • X. Ren and J. Wei, Many droplet pattern in the cylindrical phase of diblock copolymer morphology, Reviews in Mathematical Physics, Vol 19, No. 8 (2007), 879-921.

  • X. Ren and J. Wei, Single droplet pattern in the cylindrical phase of diblock copolymer morphology, Journal of Nonlinear Science, Vol 17, No. 5 (2007), 471-503.

  • E. N. Dancer, X. Ren and S. Yan, On multiple radial solutions of a singularly perturbed nonlinear elliptic system, SIAM Journal on Mathematical Analysis, Vol. 38, No. 6 (2007), 2005-2041.

  • X. Ren and J. Wei, Existence and stability of spherically layered solutions of the diblock copolymer equation, SIAM Journal on Applied Mathematics, Vol. 66, No. 3 (2006), 1080-1099.

  • X. Ren and J. Wei, Droplet solutions in the diblock copolymer problem with skewed monomer composition, Calculus of Variations and Partial Differential Equations, Vol. 25, No. 3 (2006), 333-359.

  • R. Choksi and X. Ren, Diblock copolymer/homopolymer blends: derivation of a density functional theory, Physica D, Vol. 203, No. 1-2 (2005) 100-119.

  • X. Ren and J. Wei, Wriggled lamellar solutions and their stability in the diblock copolymer problem, SIAM Journal on Mathematical Analysis, Vol. 37, No. 2 (2005), 455-489.

  • X. Ren and J. Wei, Nucleation in the FitzHugh-Nagumo system: interface-spike solutions, Journal of Differential Equations, Vol. 209, No. 2 (2005), 266-301.

  • X. Ren and J. Wei, Stability of spot and ring solutions of the diblock copolymer equation, Journal of Mathematical Physics, Vol. 45, No. 11 (2004), 4106-4133.

  • A. Chmaj and X. Ren, Soliton-stripe patterns of a functional with an attractive-repulsive-attractive interaction, Journal of Dynamics and Differential Equations, Vol. 16, No. 2 (2004), 455-468.

  • X. Ren and J. Wei, Chiral symmetry breaking and the soliton-stripe pattern in Langmuir monolayers and smectic films, Nonlinearity, Vol. 17, No. 2 (2004), 617-632.

  • X. Ren and J. Wei, The soliton-stripe pattern in the Seul-Andelman membrane, Physica D, Vol. 188, No. 3-4 (2004), 277-291.

  • X. Ren and J. Wei, Soliton-stripe patterns in charged Langmuir monolayers, Journal of Nonlinear Science, Vol. 13, No. 6 (2003), 603-624.

  • R. Choksi and X. Ren, On the derivation of a density functional theory for microphase separation of diblock copolymers, Journal of Statistical Physics, Vol. 113, No. 1-2 (2003), 151-176.

  • X. Ren and J. Wei, On energy minimizers of the di-block copolymer problem, Interfaces and Free Boundaries, Vol. 5, No. 2 (2003), 193-238.

  • X. Ren and J. Wei, On the spectra of 3-D lamellar solutions of the diblock copolymer problem, SIAM Journal on Mathematical Analysis, Vol. 35, No. 1 (2003), 1-32.

  • X. Ren and J. Wei, Triblock copolymer theory: Ordered ABC lamellar phase, Journal of Nonlinear Science, Vol. 13, No. 2. (2003), 175-208.

  • X. Ren and J. Wei, Triblock copolymer theory: Free energy, disordered phase and weak segregation, Physica D, Vol. 178, No. 1-2 (2003), 103-117.

  • X. Ren and J. Wei, Concentrically layered energy equilibria of the di-block copolymer problem, European Journal of Applied Mathemaics, Vol. 13, No. 5 (2002), 479-496.

  • A. Chmaj and X. Ren, The nonlocal bistable equation: Stationary solutions on a bounded interval, Electronic Journnal of Differential Equations, Vol. 2002, No. 03 (2002), 1-21.

  • A. Chmaj and X. Ren, Pattern formation in the nonlocal bistable equation, Methods and Applications of Analysis, Vol. 8, No. 3 (2001), 369-386.

  • A. Chmaj and X. Ren, Multiple layered solutions of the nonlocal bistable equation, Physica D, Vol. 147, No. 1-2 (2000), 135-154.

  • X. Ren and L. Truskinovsky, Finite scale microstructures in 1-D elasticity, Journal of Elasticity, Vol. 59, No. 1-3 (2000), 319-355.

  • X. Ren and J. Wei, On the multiplicity of solutions of two nonlocal variational problems, SIAM Journal on Mathematical Analysis, Vol. 31, No. 4 (2000), 909-924.

  • A. Chmaj and X. Ren, Homoclinic solutions of an integral equation: Existence and stability, Journal of Differential Equations, Vol. 155, No. 1 (1999), 17-43.

  • X. Ren, Multi-layer local minimum solutions of the bistable equation in noncylindrical domains, Journal of Differential Equations, Vol. 141, No. 1 (1997), 13-24.

  • X. Ren and M. Winter, Young measures in a nonlocal phase transition problem, Proceedings of the Royal Society of Edinburgh, 127A, No. 3 (1997), 615-637.

  • X. Ren, A variational approach to multiple layers of the bistable equation in long tubes, Archive for Rational Mechanics and Analysis, Vol. 138, No. 2 (1997), 169-203.

  • P.W. Bates, P.C. Fife, X. Ren and X. Wang, Traveling waves in a convolution model for phase transitions, Archive for Rational Mechanics and Analysis, Vol. 138, No. 2 (1997), 105-136.

  • P.W. Bates and X. Ren, Heteroclinic orbits for a higher order phase transition problem, European Journal of Applied Mathematics, Vol. 8, No. 2 (1997), 149-163.

  • P.W. Bates and X. Ren, Transition layer solutions of a higher order model in an infinite tube, Communications in Partial Differential Equations, Vol. 21, No. 1-2 (1996), 195-220.

  • X. Ren and J. Wei, Single-point concentration and least-energy solutions, Proceedings of the American Mathematical Society, Vol. 124, No. 1 (1996), 111-120.

  • X. Ren and J. Wei, Asymptotic behavior of energy solutions to a two dimensional semilinear problem with mixed boundary condition, Nonlinear Analysis: Theory, Methods, and Applications, Vol. 24, No. 4 (1995), 587-604.

  • X. Ren and J. Wei, Counting peaks of solutions to some quasilinear elliptic equations with large exponents, Journal of Differential Equations, Vol. 117, No. 1 (1995), 28-55.

  • X. Ren and J. Wei, On a semilinear elliptic equation in $R^{2}$ when the exponent approaches infinity, Journal of Mathematical Analysis and Applications, Vol. 189, No. 1 (1995), 179-193.

  • X. Ren and J. Wei, On a two dimensional elliptic problem with large exponent in nonlinearity, Transactions of the American Mathematical Society, Vol. 343, No. 2 (1994), 749-763.

  • X. Ren, Least-energy solutions to a non-autonomous semilinear problem with small diffusion coefficient, Electronic Journal of Differential Equations, Vol. 1993, No. 05 (1993), 1-21.