Tianyuan XU
,
Chunhua JIN
,
Shanming JI
. DISCONTINUOUS TRAVELING WAVE ENTROPY SOLUTIONS OF A MODIFIED ALLEN-CAHN MODEL[J]. Acta mathematica scientia, Series B, 2017
, 37(6)
: 1740
-1760
.
DOI: 10.1016/S0252-9602(17)30104-2
[1] Allen S M, Cahn J W. A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening. Acta Metall, 1979, 27:1085-1095
[2] Barbera E, Currò C, Valenti G. On discontinuous travelling wave solutions for a class of hyperbolic reactiondiffusion models. Physica D, 2015, 308:116-126
[3] Bertsch M, Passo R D. Hyperbolic phenomena in a strongly degenerate parabolic equation. Arch Rat Mech Anal, 1992, 117:349-387
[4] Cahn J W, Hilliard J E. Free energy of a nonuniform system, I:interfacial free energy. J Chem Phys, 1958, 28(2):258-267
[5] Chmaj A, Ren X. Multiple layered solutions of the nonlocal bistable equation. Physica D, 2000, 147:135-154
[6] Dickman R. Discontinuous phase transition in a dimer lattice gas. J Chem Phys, 2012, 136:4678-4686
[7] Galenko P K, Sanches F I, Elder K R. Traveling wave profiles for a crystalline front invading liquid states:analytical and numerical solutions. Physica D, 2015, 308:1-10
[8] Garrione M, Sanchez L. Monotone traveling waves for reaction-diffusion equations involving the curvature operator. Bound Value Probl, 2015, 2015:1-31
[9] Holden H, Karlsen K H, Mitrovic D, Panov E Y. Strong compactness of approximate solutions to degenerate elliptic-hyperbolic equations with discontinuous flux function. Acta Math Sci, 2009, 29B(6):1573-1612
[10] Jordan P M. Growth and decay of shock and acceleration waves in a traffic flow model with relaxation. Physica D, 2005, 207:220-229
[11] Kruzhkov S N. First order quasilinear equations in several independent variables. Mat Sb, 1970, 81:228-255(English transl Math USSR-Sb, 1970, 10:217-243)
[12] Landman K A, Pettet G J, Newgreen D F. Chemotactic cellular migration:smooth and discontinuous travelling wave solutions. SIAM J Appl Math, 2003, 63(5):1666-1681
[13] Li M, Geng H, Long F et al. Discontinuous structural phase transition of Sn-Bi melts. J Mol Liq, 2015, 204:27-32
[14] Liu H X, Pan T. Pointwise convergence rate of vanishing viscosity approximations for scalar conservation laws with boundary. Acta Math Sci, 2009, 29B(1):111-128
[15] Mai D T. Traveling waves of an elliptic-hyperbolic model of phase transitions via varying viscositycapillarity. J Differ Equ, 2011, 251:439-456
[16] Pang P, Wang Y H, Yin J X. Free-boundary problem for a singular diffusion equation. J Math Anal Appl, 2002, 265:414-429
[17] Passo R D. Uniqueness of the entropy solution of a strongly degenerate parabolic equation. Commun Partial Differ Equ, 1993, 18:265-279
[18] Rosenau P. Free-energy functionals at the high-gradient limit. Phys Rev A, 1990, 41:2227-2230
[19] Tacan F, Bekir A. Travelling wave solutions of the Cahn-Allen equation by using first integral method. Appl Math Comput, 2009, 207:279-282
[20] Wang C, Yin J, Wang Z. Similar entropy solutions of a singular diffusion equation. Comput Math Appl, 2005, 49:1059-1068
[21] Wang C, Yin J, Lu B. Anti-shifting phenomenon of a convective nonlinear diffusion equation. Discrete Contin Dyn Syst Ser B, 2010, 3:1211-1236
[22] Wu Z Q, Yin J X. Some properties of functions in BVx and their applications to the uniqueness of solutions for degenerate quasilinear parabolic equations. Northeastern Math J, 1989, 5:395-422
[23] Yin J X, Jin C H. Travelling wavefronts for a non-divergent degenerate and singular parabolic equation with changing sign sources. Proc R Soc Edinb Sect A-Math, 2009, 139:1179-1207
[24] Yin J X, Li H L, Pang P Y H. BV solutions of a singular diffusion equation. Math Nachr, 2003, 253:92-106
