PUBLICATIONS (“*” means the paper was peer-reviewed before publication)

 

1.           *The classical solutions for nonlinear parabolic integrodifferential equations,

                Journal of Integral Equations and Applications, 1 (1988), 249-263.

 

2.           *On the existence of the weak solution and the regularity of the free boundary to a one-dimensional two-phase Stefan problem, (with J.R. Cannon),

            Journal of Differential Equations, 73 (1988), 104-118.

 

3.           *A uniqueness theorem for a class of nonlinear parabolic inverse problems, (with J.R. Cannon),  Inverse Problems, 4 (1988), 411-416.

 

4.           *The classical solution of the periodic Stefan problem,

              Journal of Partial Differential Equations, 1 (1988), 43-60.

 

5.           *A class of nonlinear nonclassical parabolic problems, (with J.R. Cannon),

              Journal of Differential Equations, 79 (1989), 266-288.

 

6.           *A uniqueness theorem for nonclassical parabolic problems,

              Applicable Analysis, 34 (1989), 67-78.

 

7.           *An iteration procedure for a class of integrodifferential equations of parabolic type, (with J.M. Chadam), Journal of Integral Equations and Applications, 2 (1989), 31-47.

 

8.           A class of multidimensional nonclassical parabolic equations, “Theory and Applications of Differential Equations”, (Ed. A.R. Aftabizadel), Vol. 1, Ohio University Press, (1989), 122-127.

 

9.           A degenerate free boundary problem arising from the moisture evaporation in partially saturated media, “Continuum Mechanics and Its Applications”, (Ed. G.A.C. Graham), Hemisphere Publishing Corp., NY, (1989), 621-629.

 

10.       *A periodic free boundary problem arising from chemical reaction-diffusion processes, (with J.R. Cannon), Nonlinear Analysis, TMA, 15 (1990), 939-948.

 

11.       *A parabolic inverse problem with an unknown boundary condition, (with W. Rundell), Journal of Differential Equations, 86 (1990), 234-242.

 

12.       *Numerical solutions of some parabolic inverse problems, (with J.R. Cannon), Numerical Methods for Partial Differential Equations, 6 (1990), 177-191.

 

13.       *The determination of an unknown function in a parabolic equation with an over-specified condition, (with J.M. Chadam), Mathematical Methods in Applied Sciences, 13 (1990), 421-430.

 

14.       The Cauchy problem for nonlinear degenerate integrodifferential equations of parabolic type, “Ocean waves mechanics computational fluid dynamics and Mathematical Modelling”, (Ed. M. Rahman), Comput. Mech. Pul., Boston, (1990), 481-488.

 

15.       *On nonlinear parabolic equations with nonlinear trace type functionals, (with J.R. Cannon), Inverse Problems, 7 (1991), 149-161.

 

16.       *A mixed type boundary value problem describing the propagation of the disturbances in viscous media, (with Y. Lin), Differential and Integral Equations, 4 (1991), 639-646.

 

17.       *A free boundary problem describing an irreversible crystallization process, Differential and Integral Equations, 4 (1991), 869-882.

 

18.       *On parabolic Volterra equations in several space dimensions, SIAM Journal on Mathematical Analysis, 22 (1991), 1723-1737.

 

19.       *Global solvability for some parabolic inverse problems, Journal of Math. Anal. and Applications, 162 (1991), 392-403.

 

20.       *Regularity of interfaces in the Stefan problem with mushy region, Canadian Mathematical Bulletin, 35 (1992), 136-144.

 

21.       *The solvability for a class of nonlinear integrodifferential equations of parabolic type, Journal of Partial Differential Equations, 5 (1992), 46-60.

 

22.       *A class of nonlinear parabolic equations with some nonlinear functionals, (with Y. Lin), Journal of Math. Analysis and Applications, 168 (1992), 28-41.

 

23.       *A singular-degenerate free boundary problem arising from the moisture evaporation in partially saturated media, Annali di Matemateca, Pura ed Appl., Vol. CLXI (1992), 379-397.

 

24.       *The blowup property of solutions to a class of diffusion equations with nonlinear localized reactions, (with J.M. Chadam, A. Pierce), Journal of Math. Analysis and Applications, 169 (1992), 313-328.

 

25.       *Weak and classical solutions of some Volterra integrodifferential equations, Communication in P.D.E., 17 (1992), 1369-1385.

 

26.       *Remarks on regularity of the interface in the heat equation with strong absorption, in “Progress in Partial Differential Equations: Elliptic and Parabolic Problems”, (ed. by C. Bandle), John Wiley & Sons, Inc., New York, (1992), 284-289.

 

27.       *The Lipschitz continuity of the interface in the heat equation with strong absorption, Nonlinear Analysis, TMA., 20 (1993), 413-416.

 

28.       *Existence for one-dimensional nonlinear parabolic Volterra integrodifferential equations, (with Y. Lin), Journal of Integral Equations and Applications, 5 (1993), 75-83.

 

29.       *Determination of the leading coefficient a(x) in the heat equation ut = a(x)   u, (with Bei Hu), Quarterly of Applied Mathematics, LI (1993), 577-583.

 

30.       The Stefan problem in material with memory (with J.M. Chadam), in “Free boundary problems involving solids”, (ed. by J.R. Chadam), John Wiley & Sons, Inc., New York, (1993), 117-123.

 

31.       *Blowup and global existence for a nonequilibrium phase change process, in Variational and Free Boundary Problems”, (ed. by A. Friedman and J. Spruck), Springer-Verlag New York, Inc., (1993), 195-204.

 

32.       *A diffusion equation with localized reactions, (with J. Chadam), Proceeding of Edinburgh Mathematical Society, 37 (1994), 101-118.

 

33.       *Global solutions of Maxwell’s equations in an electromagnetic field with the temperature-dependent electrical conductivity, European Journal of Applied Mathematics, 5 (1994), 57-64.

 

34.       *Global solutions and quenching to a class of quasilinear parabolic equations, (with Bei Hu), Forum Mathematicum, 6 (1994), 371-383.

 

35.       *The profile near blowup time for solution of the heat equation with a nonlinear boundary condition, (with Bei Hu), Transaction of American Mathematical Society, 346 (1994), 117-136.

 

36.       Blowup of Solution for the Heat Equation with a Nonlinear Boundary Condition, in Proceeding of Symposium on Comparison Methods and Stability Theory, Marcel-Dekker, Inc., New York, (1994), 189-198.

 

37.       *Blowup versus Global existence for a class of nonlinear parabolic equations, Nonlinear Analysis, TMA, 23 (1994), 911-924.

 

38.       *Recent and New Results on determination of unknown coefficients in parabolic equations with over-specified conditions, SIAM proceeding  in “Inverse problems in diffusion processes” (Eds. H. Engl and W. Rundell), SIAM, Philadelphia, (1995), 181-198.

 

39.       *On a class of semilinear equations with prescribed energy, (with Bei Hu), Rendiconti del Circolo Matematico di Palermo, XLIV (1995), 479-505.

 

40.       *The semiconductor system with temperature effect, Journal of Math. Analysis and Applications, 196 (1995), 135-152.

 

41.       *A free boundary problem arising from stress-driven diffusion in polymers, Discrete and Continuous Dynamical Systems, 2 (1996), 191-202.

 

42.       *Critical Exponents for a System of Heat Equations coupled in a Nonlinear Boundary Condition (with Bei Hu), Mathematical Methods in Applied Science, 19 (1996), 1099-1120.

 

43.       *Solvability of a Class of Parabolic Inverse Problems, Advances in Differential Equations, 1 (1996), 1005-1024.

 

44.       *On Critical Exponents for the Heat Equation with a Nonlinear Boundary Condition, (with Bei Hu), Analyse non Lineaire, Annales de L’institute henri Poincare, 13 (1996), 707-732.

 

45.       *L2,u-estimates for parabolic equations and applications, Journal of Partial Differential Equations, 10 (1997), No. 1, 31-44.

 

46.       *The DeGiorgi-Nash-Moser type of estimate for parabolic Volterra integrodifferential equations (with Bei Hu), Pacific Journal of Mathematics, 15 (1997), 265-277.

 

47.       *Finite difference approximations for a class of nonlocal parabolic equations, (with Yanping Lin and Shuzhan Xu), International Journal of Mathematics and Mathematical Sciences, 20 (1997), 147-164.

 

48.       *On critical exponents for the heat equation with a mixed nonlinear Dirichlet-Neumann boundary conditions, (with Bei Hu), Journal of Mathematical Analysis and Applications, 209 (1997), 683-711.

 

49.       *Regularity of Solutions to Maxwell’s System in Quasi-Stationary Electromagnetic Fields and Applications, Communication in P.D.E., 22 (1997), No. 7 & 8, 1029-1053.

 

50.       *On Maxwell’s equations in an electromagnetic field with a temperature effect, II, (with Robert Glassey), in Communication in Math. Physics, 194 (1998), 343-358.

 

51.       *A Chemical Diffusion Process with Reaction Taking Place at Free Boundary, (with S. Ding and Y. Tao), Canadian Applied Math. Quarterly, 5 (1998), 49-74.

 

52.       *On Maxwell’s equations in an electromagnetic field with the temperature effect, SIAM Journal of Mathematical Analysis, 29 (1998), 637-651.

 

53.       *Blowup of Solutions for Parabolic Equations with Nonlocal Functionals, (with J.R. Cannon), Advances in Mathematical Sciences, 3 (1998), No. 1.

 

54.       *Some remarks on Maxwell’s system in quasi-stationary electromagnetic fields, Proceedings of the International Conference on Dynamical System and Differential Equations, Vol. II, (1998), 353-358.

 

55.       *On a singular limit problem for nonlinear Maxwell’s equations,

           Journal of Differential Equations, 156 (1999), 355-375.

 

56.       *On a p-Laplacian type of evolution system and applications to the Bean model in the type-II superconductivity theory, Quarterly of Applied Mathematics, Vol. LIX, No. 1, (2000), 47-66.

 

57.       *On Maxwell’s System with a thermal effect, (with Jeff Morgan),

                   Discrete and Dynamical Systems,  series B, vol. 1 (2001), 485-494.

 

58.       *On a free boundary problem with superheating arising in microwave heating processes, Advances in Mathematical Sciences and Applications,  vol.12(2002), 409-433.

 

59.       *Optimal regularity of solution to a degenerate elliptic system arising in electromagnetic fields, Communication on Pure and Applied Analysis, vol. 1 (2002), 127-134.

 

60.              *A Degenerate Evolution System Modeling Bean’s Critical-State Type-II Superconductors (with Ben Q. Li, Jun Zou), Discrete and Dynamical Systems Serie A, Vol.8(2002), 781-794.

 

61.              *Optimal Control of Microwave Sterilization in Food Processing (with J. Tang, BenQ   Li), International Journal of Applied Mathematics,Vol.10(2002), 13-31.

 

62.     On Professor John R. Cannon’s Research Accomplishments

          (with Richard E.  Ewing, Yanping Lin),

       Dynamics of Continuous, Discrete and Impulsive Systems,

         Series A:   Mathematical Analysis, 10 (2003), 635-647.

 

63. Progress in Partial Differential Equations and Applications,

One of the editors (with R. Dillon, A.   Khapalov, V.S. Manoranjan) for a special issue of Dynamics of Continuous, Discrete and Impulsive Systems,

             Vol.10, Number 5, 2003.

 

64. *Regularity of Weak Solution to Maxwell’s Equations and Applications to

        Microwave Heating,

      Journal of Differential Equations, 200(2004), 137-161.

 

65. *On a class of Parabolic Equations with Nonlocal Boundary Conditions,

      Journal of Mathematical Analysis and Applications,

      Vol. 294(2004), 712-728.

 

66. *On a Nonlinear Maxwell’s Equation in Quasi-stationary Fields,

  Mathematical Methods and Modeling in Applied Sciences,

  Vol.14 (2004), 1521-1539.

 

67. *On a Phase-Field Model for a Melting Problem Arising in Induction Heating 

        Processes,

      Nonlinear partial differential equations and their applications, 368--375,

     GAKUTO     Internat. Ser. Math. Sci. Appl., 20, Gakk\=otosho, Tokyo, 2004.

 

68. *On a phase-change problem arising from inductive heating.

        WSU Technical Report Series, 2003-06,

        to appear in the journal of  Nonlinear Differential Equations and Applications,

       (in press).

 

69.  *Global Solvability to a Singular Nonlinear Maxwell’s Equation in Quasi-stationary

        Electromagnetic Fields (with Wei Wei),

         Communication in Pure and Applied Analysis, vol.4 (2005), 431-444.

 

70. Numerical Solutions to Bean's Critical-State Model for Type-II Superconductors,

      (with Wei Wei),

      International Journal of Numerical Analysis and Modeling, vol 2(2005), 479-488.

 

71. On Two-Phase Stefan Problem Arising from a Microwave Heating Process,

      (with R. V. Manoranjan, R. Showalter )

      

       Continuous and Discrete and Dynamical Systems, Serie A, vol.15(2006),

       1155-1168.

 

72. Regularity of Weak Solution to a p-curl system,

   Differential and Integral Equations, Volume 19(2006),Number 4, 361-368

 

73.              Global Solvability for a Nonlinear semi-static Maxwell’s equations,

       (with Guofu Lu)

             Journal of Partial Differential Equations, , Volume 19(2006), 113-125.

 

74. Heat Transfer characteristics of mixed electro-osmotic and pressure driven flow 

     (with P. Dutta, K. Horiuchi).

 

To  appear in “Computers and mathematics with applications”.

 

 

75. Existence and Regularity of Weak Solution to Maxwell's Equations with

       a Thermal Effect, 

 

  Mathematical Methods in applied analysis, vol.29(2006), 1199-1213.

 

 
Paper Submitted for Publication

 

 

76. Fundamental solution for the heat equation with nonlinear convection,

      (with Guofu Lu), submitted for publication.

 

 

77. Numerical solutions for a coupled system arising from induction heating

    (with Dong Sun, V.S. Manoranjan), submitted for publication.

 

78. A free boundary problem arising in induction heating model.

          Submitted for publication.

 

79. On  a degenerate parabolic system

 

     In preparation.

 


Other Scholar Publication

 

        Maxwell’s Equations in Electromangetic Fields.

 

        Lecture Notes, Washington State University (2005)