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),
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),
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.
A class of multidimensional nonclassical parabolic equations, “Theory and Applications of Differential Equations”, (Ed. A.R. Aftabizadel), Vol. 1,
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.
parabolic inverse problem with an unknown boundary condition, (with
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.
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.,
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.
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,
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.
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.,
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.
and New Results on determination of unknown coefficients in parabolic equations
with over-specified conditions,
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.
Chemical Diffusion Process with
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,
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.
63. Progress in Partial Differential Equations and Applications,
One of the editors (with R.
Dillon, A. Khapalov, V.S.
Vol.10, Number 5, 2003.
64. *Regularity of Weak Solution to Maxwell’s Equations and Applications to
72. Regularity of Weak Solution to a p-curl system,
Differential and Integral Equations, Volume 19(2006),Number 4, 361-368
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”.