(40 peer-reviewed papers published; 1 peer-reviewed paper accepted for publication)

Department of Mathematical Sciences

George Mason University

Thank you, parents and students, for the interest in our program. This program has been running since 1994 summer. It is the 3rd longest running program for youth at George Mason University. The 2018 Summer program , which is the 25th summer (yes, a quarter of century) that we run this program, has been concluded and we have a wonderful turnout of the students. Thank you, parents and students, for the continuing support of this program.

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**The list of Professor J. E. Lin's publications** **(peer-reviewed)**

- (with Isah Bala Yabo and Basant Kumar Jha) On a Couette flowof conducting fluid. International Journal of Theoretical and Applied Mathematics, Volume 4, Issue 1 (2018) 8-21.
- On elliptic equations with combined nonlinearities. Applied Analysis and Optrimization, Volume 2, Number 1 (2018) 87-92.
- On a system of nonlinear optical wave equations in two-spatial dimension. Journal of Mathematics Research, Volume 10, Number 2 (2018) 100-103.. .
- (with Basant Kumar Jha and Isah Bala Yabo) "Transient Natural Convection in an Annulus with Thermal Radiation". Applied Mathematics, Volume 8, Number 9 (2017) 1351-1366
- "Nonexistence of nontrivial solutions with decay order for some nonlinear elliptic equations", Journal of Nonlinear and Convex Analysis, Volume 18, Number 5 (2017) 883-892.
- "Nonexistence of Nontrivial Solutions with Decay Order for a Biharmonic P-Laplacian Equation and System". Applied Mathematics, Volume 8, Number 7 (2017) 920 - 928.
- (with Chun-Te Lee, Chun-Che Lee, and Mei-Li Liu) "Some Remarks on the Stability Condition of Numerical Scheme of the KdV-type Equation". Journal of Mathematics Research, Volume 9, Issue 4 (2017) 11 - 22.
- "Nonexistence of Nontrivial Stationary Solutions with Decay Order for Some Nonlinear Evolution Equations". Journal of Mathematics Research Volume 9, Issue 3 (2017) 1-7.
- "On the Nonexistence of Nontrivial Solutions for Some P-Laplacian Equations". Applied Mathematical Sciences Volume 11, Issue 22 (2017) 1057-1066.
- (with Isah Bala Yabo and Basant Kumar Jha) "Combined Effects of Thermal Diffusion and Diffusion-thermo Effects on Mass Transfer Flow in a Vertical Channel with Thermal Radiation". Applied Mathematics 7 (2016) 2354-2373.

- (with Chun-Te Lee, Chun-Che Lee, and Mei-Li Liu) "On the numerical modeling of capillary flow dynamics in a microchannel model using finite element method". Journal of Applied Mechanics and Technical Physics, Volume 57, Issue 5, (2016) pp. 937-948..
- (with Manal Badgaish,and Padmanabhan Seshaiyer) "Nonlinear Dynamics and Analysis of Intracranial Saccular Aneurysms with Growth and Remodeling".Journal of Nonlinear Dynamics, (2016) Article ID 2869083, http://dx.doi.org/10.1155/2016/2869083
- “Time Decay for the Solutions of a Fourth-Order Nonlinear Schrodinger Equation”. Contemporary Mathematics, Volume 581 (2012), pp. 169-174.
- “Local Time Decay for a Quasilinear Schrödinger Equation" Methods and Applications of Analysis, 16, (2009), 313 – 320.
- (with Blane Laubis) “Optimal Investment Allocation in a Jump Diffusion Risk Model with Investment: A Numerical Analysis of Several Examples” . 2008 Actuarial Research Conference Proceedings, appeared on ARCH 2009 (Electronic). http://www.soa.org/news-and-publications/publications/proceedings/arch/arch-2009-iss1.aspx
- “Local time decay for a nonlinear beam equation” Methods and Applications of Analysis, Volume 11, No. 1 (2004) pp. 65 – 68.
- (with H. H. Chen) “On a direct construction of inverse scattering problems for integrable nonlinear evolution equations in the two-spatial dimension” , International Journal of Mathematics and Mathematical Sciences, Volume 2004, No. 58 (2004) pp. 3117-3128.
- (with H. H. Chen) “On the integrability of nonlinear evolution equations in two-spatial dimensions” . Proceedings of ICCM2001, New Studies in Advanced Mathematics. Vol.4 (International Press, Somerville, MA) (2004) pp. 659-664
- (with E. Bosch) “Wavelet-based dimension reduction for hyperspectral image classification” in Algorithms and Technologies for Multispectral Hyperspectral, and Ultraspectral Imagery, Proceedings of SPIE Vol. 5093 (2003) pp. 57-69.
- "On the Symmetries, Constants of Motion, and the Hamiltonian Structure of the Modified Kadomtsev -Petviashvili Equation", Bulletin of the Institute of Mathematics, Academia Sinica 19 (1991) pp. 11-19.
- (with H. H. Chen) "On the Integrability of Nonlinear Evolution Equations", Nonlinaer Semigroups, Partial Differential Equations, and Attractors, edited by T. L. Gill and W. W. Zachary, Lecture Notes in Mathematics, Vol. 1394 (1989) pp. 30-43.
- (with H. H. Chen) "Integrability of Nonlinear Wave Equations", Integrability in Dynamical Systems, edited by J. Buchler, J. Ipser, and C. Williams, Annals of the New York Academy of Sciences, 536 (1988) pp. 91-99.
- (with H. H. Chen) "Factorization of the Recursion Operators and the Integrability of Nonlinear Evolution Equations" , Topics in Soliton Theory and Exactly Solvable Nonlinear Equations, edited by M. Ablowitz, B. Fuchssteiner, and M. Kruskal (World Scientific Publishing Co., 1987) pp. 97-107.
- (with H. H. Chen) "On the Infinite Hierarchies of Symmetries of Symmetries and Constants of Motion for the Kadomtsev-Petviashvili Equation" , Physica D, 26 (1987) 171-180.
- (with H. H. Chen) "On the Integrability of Multidimensional Nonlinear Evolution Equations", Journal of Mathematical Physics, 28 (1987) 347-350.
- (with H. H. Chen and Y. C. Lee) "On the Direct Construction of the Inverse Scattering Operators of Integrable Nonlinear Hamiltonian Systems" , Physica D, 26(1987) 165-170.
- "Asymptotic Behavior in Time of the Solutions of a System of Multidimensional Coupled Nonlinear Schrödinger Equations", Tamkang Journal of Mathematics, 17 (1986) 27-30.
- "Local Energy Decay for waves Governed by a System of Nonlinear Schrödinger Equations in a Nonuniform Medium", International Journal of Mathematics and Mathematical Sciences, 8 (1985) 621-623.
- (with H. H. Chen and Y. C. Lee) "A New Hierachy of Symmetries for the Integrable Nonlinear Evolution Equations", Advances in Nonlinear Waves, Volume II, edited by L Debnath (Pitman, New York, 1985) pp. 233-239.
- "On a Nonlinear Modulated Dispersive Wave" Proceedings of the National Science Council of the Republic of China, 8 (1984) 129-131.
- (with H. H. Chen and Y. C. Lee) "On a New Hierarchy of Symmetries for the Kadomtsev-Petviashvili Equation" , Physica D, 9 (1983) 439-445.
- (with H. H. Chen and Y. C. Lee) "On a New Hierarchy of Symmetries for the Benjamin-Ono Equation" , Physics Letters A, 91 (1982) 381-383.
- "Decay of the Local Energy of a Two-dimensional Wave in a Nonlinear Weakly Negative Dispersive Medium", Physics Letters A, 91 (1982) 278-279.
- (with H. H. Chen) "Constraints and Conserved Quantities of the Kadomtsev-Petviashvili Equations", Physics Letters A, 89 (1982) 163-167.
- (with H. L. Hwang, D. C. Liu, and J. J. Loferski) "Numerical Analkysis of Junction-depth Effect in the Grating-type Si Solar Cell", Journal of Applied Physics, 52 (1981) 1548-1551.
- "On the Generalized Korteweg-de Vries Equation", Manuscripta Mathematica, 30 (1980) 417-423.
- "Superexponential Decay of Solutions of a Semilinear Wave Equation",Journal of Functional Analysis, 31 (1979) 321-332.
- (with Walter Strauss) "Decay and Scattering of Solutions of a Nonlinear Schrödinger Equation", Journal of Functional Analysis, 30 (1978) 245-263.
- "Asymptotic Behavior in Time of the Solutions of Three Nonlinear Partial Differential Equations", Journal of Differential Equations, 29 (1978) 467-473
- (with Elfriede Wenzelburger) "Reduction of all three-term syzygies". Publicationes Mathematicae Debrecen, 21 (1974) 57-59..