## LIST OF PUBLICATIONS

### Yanping Lin

#### JOURNAL PUBLICATIONS

 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998

1. On the Stability of the temperature distribution in acomposite heat conductor with mixed boundary value conditions(with J. Cannon) , Bollettino,U.M.I. (7) 1-B, (1987) 453-47

2. Determination of a parameter $p(t)$ in some quasi-linear parabolic equations (with J. Cannon), Inverse Problem, 4 (1988) 35-45.

3. Determination of a parameter $p(t)$ in some H\"{o}lder classes for semi-linear parabolic equations (with J. Cannon), Inverse Problem, 4 (1988) 595-606.

4. A mixed boundary problem describing the propagation of disturbances in viscous media. I. Weak solutions for quasi-linear equations, J. Math. Anal. Appl., Vol. 135, No. 2, (1988) 644-653.

5. Classical and weak solutions for one-dimensional pseudo- parabolic equation with typical boundary data (with J. Cannon), Annali di Mathematica Pure ed Applicata, (IV), Vol. CLII, (1988) 375-385.

6. A mixed boundary problem describing the propagation of disturbances in viscous media. Smooth solutions for general linear equations, Chinese Journal of Mathematics, Vol. 16, No. 2, (1988) 67-80.

7. Non-classical $H^1$ projection and Galerkin methods for nonlinear parabolic integrodifferential equations (with J. Cannon), Calcolo, Vol. 25, No. 3 (1988) 187-201.

8. Smooth solution for an integro-differential equation of parabolic type (with J. Cannon), Differential and Integral Equations, Vol. 2, No. 1, (1989) 111-121.

9. A finite difference solution to an inverse problem for determining a control function in a parabolic partial differential equation (with S. Wang), Inverse Problems, 5(1989) 631-640.

10. Quasi-linear parabolic equations with nonlocal boundary conditions (with J. Cannon and J. van der Hoek), Rendiconti di Matematica , Serie VII, Vol. 9 Roma (1989) 239-264.

11. Galerkin methods and $L^2$ error estimates for hyperbolic integro-differential equations (with J. Cannon and C. Xie), Calcolo , Vol. 26 (1989) 197-206.

12. A numerical method for diffusion equation with nonlocal boundary specifications (with S. Wang), Int. J. Engng. Sci. , Vol 28, N0. 6 (1990) 543-546.

13. An implicit finite difference scheme for the diffusion equation subject to mass specification (with J. Cannon and S. Wang), Int. J. Engng. Sci. , Vol. 28, No. 7 (1990) 573-578.

14. A Galerkin procedure for diffusion equations with integral boundary conditions (with J. Cannon), Int. J. Engng. Sci. , Vol. 28, No. 7 (1990) 579-587.

15. An inverse problem of finding a parameter in semi-linear heat equations (with J. Cannon), J. Math. Anal. Appl., Vol. 145, No. 2 (1990) 470-484.

16. A priori $L^2$ error estimates for finite element methods for nonlinear diffusion equations with memory (with J. Cannon), SIAM J. Numer. Anal. Vol. 27, No. 3 (1990) 595-607.

17. A lumped mass finite element method for nonlinear parabolic integro-differential equations (with T. Zhang), Numer. Math., A J. Chinese Univ., No 4 (1990) 342-354.

18. Galerkin method for nonlinear parabolic integro-differential equations with non-linear boundary conditions, SIAM J. Numer. Anal. Vol. 27, No. 3 (1990) 608-621.

19. On stability of nonclassical elliptic projection and applications (with T. Zhang),\\ Numer. Math., A J. of Chinese Univ., No. 3 (1990) 230-238.

20. Galerkin methods for nonlinear Sobolev equations, Aequationes Mathematicae, 40 (1990) 54-66.

21. A priori $L^2$ error estimates for Galerkin methods for nonlinear Sobolev Equations, Journal of System Sciences and Mathematical Sciences., Vol. 3 (1990) 126-135.

22. An inverse problem for a class of quasilinear parabolic equations, SIAM J. Math. Anal., Vol. 22, No. 1 (1991) 146-156.

23. The Stability of Ritz-Volterra projection and error estimates for finite element methods for a class of integro-differential equation of parabolic type (with T. Zhang), Aplikace Matematiky, Vol. 36, No. 2 (1991) 123-133.

24. Ritz-Volterra projection onto finite element spaces and application to integro-differential and Related equations (with V. Thomee and L. Wahlbin), SIAM J. Numer. Anal. , Vol. 28, No. 4 (1991) 1047-1070.

25. A mixed boundary problem describing the propagation of disturbances in viscous media (with H. Yin), Differential and Integral equations, Vol. 4 (1991) 639-646.

26. $L^{\infty}$ error bounds for some nonlinear integro-differential equations by finite element approximations (with T. Zhang), Math. Numer. Sinica, No. 2 (1991) 177-186.

27. Non-classical elliptic projection and $L^2$ error estimates for Galerkin methods for linear integro-differential equation of parabolic type, J. Comp. Math., Vol. 9, No. 3 (1991) 238-246.

28. A remark on the solvability of non-linear parabolic integro-differential equations in one space dimension, (with J. Cannon), Bollettino, U.M.I., (7) 5-B (1991)853-874.

29. Determination of a control parameter in a parabolic partial differential equations (with J. Cannon and S. Wang), J. Australian Math. Soc., Series B., Vol. 33 (1991) 149-163.

30. Finite element methods for nonlinear Sobolev equations with nonlinear boundary conditions in multi-dimensional spaces (with T. Zhang), J. Math. Anal. Appl., Vo. 165, No. 1 (1992) 180-191.

31. Determination of Source parameter in parabolic equations (with J. Cannon and S. Wang), MECCANICA, Vol. 27 (1992) 85-94.

32. Nonlinear parabolic equations with nonlinear functionals (with H. M. Yin), J. Math. Anal. Appl., Vol 168, No. 1 (1992) 28-41.

33. Existence for one-dimensional nonlinear parabolic Volterra integrodifferential equations, (with H. M. Yin), J. Int. Eqs. Appl. Vol. 5, N. 1 (1993) 75-83 .

34. A parabolic trace type functional differential equation (with J. R. Cannon, F. B. Jones and S. Wang), J. Diff. Eqs., Vol 101 (1993) 325-331.

35. Finite difference approximations for a class of non-local parabolic boundary value problems (with R. J. Tait), International. J. Comp. Appl. Math. Vol. 47 (1993) 335-350.

36. Numerical solutions for a class of differential equations in linear viscoelasticity (with W. Allegretto), Calcolo, 30 (1993) 69-88.

37. The solution of the diffusion equation in two space variables subject to the specification of mass (with J. Cannon and A. Matheson), Appl. Anal. , Vol. 15, No. 1-2 (1993) 1-15.

38. On a Class of non-local parabolic boundary value problems (with R. Tait), Int. J. of Engng Sci., 32 (1994) 395-407.

39. Upwind finite difference schemes for a linear conservation law with memory, Numerical Methods for Partial Differential Equations, Vol 10 (1994) 475-489.

40. Numerical procedures of determination of an unknown source coefficient in semi-linear parabolic differential equations ( with J. Cannon and S. Xu) Inverse problems, Vol 10 (1994) 227-243.

41. Analytical and numerical solutions for a class of nonlocal nonlinear parabolic equations, SIAM J. Math. Anal., Vol. 25 (1994) 1577-1594.

42. Finite difference solutions for parabolic equations with time weighting initial conditions, J. Appl. Math. Comp., Vol. 64 (1994)-49-61.

#### CONFERENCE PROCEEDINGS

1. Determination of a source term in a linear parabolic differential equation with mixed boundary conditions (with J. Cannon), Inverse Problems (ed. J.R. Cannon and U. Hornung), ISNM, 77, (1986) 31-49.

2. A priori $L^2$ error estimates for Galerkin approximations for semi-linear integro-differential equatios of parabolic type, Transport Theory, Invariant Imbedding and Integral Equation (P. Nelson, et al., eds) Lecture Notes i in Pure and Applied Mathematics 115 (1989) 421-434.

3. A free boundary value problem related to the combustion of a solid: First initial-boundary value case, Differential Equations and Applications (R. Aftebizadeh, ed) Ohio University Press 1 (1989) 109-121.

4. Galerkin methods for diffusion equation with memory ( with T. Zhang), Ocean Waves Mechanics, Computational Fluid Dynamics and Mathematical Modelling, (ed. M. Rahman), Computational Mechanics Publications, (1990) 799-806.

5. A numerical method for the diffusion equation subject to nonlocal second boundary specifications (with S. Wang), Ocean Waves Mechanics, Computational Fluid Dynamics and Mathematical Modelling, ed. M. Rahman, Computational Mechanics Publications, (1990) 473-480.

6. Semi-linear heat equation subject to the specification of energy (with J. Cannon and J. Van der Hoek), Modeling and Analysis of Diffusive and Advective Processes in Geosciences (ed. W.E. Fitzgibbon and M. F. Wheeler), 40-51, Society for Industrial and Applied Mathematics, 1992

7. A finite difference domain decomposition for the heat equations in cylindrical coordinates ( with H. li and Y. S. Wong), Advances in Computer Methods for Partial Differential Equations VII (ed. R. Vichnevetsky, D. Knight and C. Richter), 441-445, IMACS, 1992.

8. Numerical solutions for integro-differential equations of parabolic type with weakly singular kernels, Comparison Methods and Stability Theory, (ed. X. Liu and D. Siegel), Lecture Notes in Pure and Applied Mathematics, Vol. 162, p261-268, New York, Marcel Dekker, 1994.

9. A finite difference scheme for an inverse heat equation (with J. Cannon and S. Xu), The Proceedings of the First World Congress of Nonlinear Analysis, (V. Lakshmikantham ed.) Walter de Gruyter, New York, 497-504 (1996) .

### Most Current Publications: 1996---

1. Semilinear integro-differential equations with nonlocal Cauchy problem (with J. Liu), Nonlinear Analysis, Vol 26, No. 5 (1996) 1023-1033.

2. A class of nonlocal parabolic problems with numerical method (with T. Zhang), Acta Mathematicae Applicatae Sinica, Vol 19, No. 2, 279-289 (1996)

3. A nonlocal parabolic system in linear thermoelasticity, Dynamics of Continuous, Discrete and Impulsive System, Vol. 2, No. 3 (1996) 267-283.

4. On maximum norm estimates for Ritz-Volterra projections and applications to some time-dependent problems, J. Comp. Math., Vol 15, N0. 2 (1997) 159-178.

5. Finite Difference approximation for a class of non-local parabolic equations (with S. Xu and H.M. Yin) Int. J. Math. \& Math. Sci., Vol. 20, No. 1 (1997) 147-164.

6. A parabolic Integro-Differential Equation Arising from Thermoelastic Contact (W. Allegretto and J. Cannon), Discrete and Continuous Dynamical Systems, Vol. 3, No. 2 (1997) 217-234.

7. A nonlocal parabolic system modeling axially symmetric thermoelastic contact of two discs, to appear in J. Math. Anal. Appl., Vol. 210, (1997) 39-57.

8. Expnential decay and stability of Volterra diffusion equations (with J. Liu and C. Ma) To appear in Volterra Equations and Applications, The proceedings of Volterra Centennial Symposium, Arlington, Texas, May 1996, (ed. C. Corduneanu and I. Sandberg)

9. Semi-discrete Finite Element Approximations for Linear Parabolic Integro-differential Equations with Integrable Kernels, To appear in J. Int. Eqs. Appl.

10. A numerical approximation of NonFickian flows with mixing length growth in porous media (with R. E. Ewing and Junping Wang)

11. $C^{\alpha, \alpha/2}$ solutions for the amorphous silicon system and related problems, (with W. Allegretto and A. Zhou) to appear in Electronic J. Diff. Eqs.