Xiaofeng Ren's publications and preprints
X. Ren and G. Zhang,
Disc–disc structure in a two-species interacting
system on a flat torus,
Journal of Nonlinear Science, Vol 32, No. 1 (February, 2022).
S. Luo, X. Ren, and J. Wei,
Nonhexagonal lattices from a two species
interacting system,
SIAM Journal on Mathematical Analysis, Vol. 52, No. 2 (2020) 1903-1942.
X. Ren and D. Shoup,
The impact of the domain boundary on
an inhibitory system: interior discs and boundary half discs,
Discrete and Continuous Dynamical Systems - Series A,
Vol. 40, No. 6 (2020) 3957-3979.
X. Ren and C. Wang,
Stationary disk assemblies in a
ternary system with long range interaction,
Communications in Contemporary Mathematics,
Vol 21, No. 06 (2019) 1850046.
X. Ren and J. Trageser,
A study of pattern forming systems with a
fully nonlocal interaction kernel of
possibly changing sign,
Physica D, Vol 393 (2019) 9-23.
C.-N. Chen, Y.-S. Choi, Y. Hu and X. Ren,
Higher dimensional bubble profiles in a sharp
interface limit of the FitzHugh-Nagumo system,
SIAM jounral on Mathematical Analysis, Vol. 50, No. 5 (2018) 5072-5095.
C.-N. Chen, Y.-S. Choi and X. Ren,
Bubbles and droplets in a singular limit of the
FitzHugh-Nagumo system,
Interfaces and Free Boundaries, Vol. 20, Issue 2 (2018) 165-211.
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.