James M. Scott

PhD Student

The University of Tennessee

Ayres Hall 314
1403 Circle Dr.
Knoxville, TN 37996
Email

Research Interests

I have used variational methods and techniques from potential theory, harmonic analysis, and compensated compactness to analyze systems of partial differential and integral equations. Much of my dissertation work contributes to the theory of a nonlocal model in continuum mechanics known as peridynamics. I have also conducted analysis of systems of hyperbolic conservation laws.

Publications and Preprints

• M. Kassmann, T. Mengesha, and J. Scott, "Solvability of Nonlocal Systems Related to Peridynamics." Communications on Pure & Applied Analysis, 18 (2019), pp. 1303-1332. Online Version
• J. Scott and T. Mengesha, "A Potential Space Estimate for Solutions of Systems of Nonlocal Equations in Peridynamics." SIAM Journal on Mathematical Analysis, 51 (2019), pp. 86-109. Online Version
• J. Scott and T. Mengesha, "A Fractional Korn-Type Inequality." Discrete and Continuous Dynamical Systems, 39(6) (2019), pp. 3315-3343. Online Version
• J. Scott, M. P. Laiu, and C. D. Hauck, "Analysis of the Zero Relaxation Limit of Systems of Hyperbolic Balance Laws with Random Initial Data." SIAM/ASA Journal of Uncertainty Quantification, 7(3) (2019), pp. 806-837. Online Version. A version with supplementary material is located here.
• T. Mengesha and J. Scott, "The Solvability of a Strongly-Coupled Nonlocal System of Equations." Journal of Mathematical Analysis and Applications, 486(2) (2020), article 123919. Online Version
• T. Mengesha and J. Scott, "Asymptotic Analysis of Solutions to a Coupled System of Nonlocal Equations with Oscillatory Coefficients." Submitted. arXiv Preprint
• J. Scott and T. Mengesha, "A Fractional Korn-Type Inequality on Bounded Domains and Applications." In preparation.

Teaching (Fall 2019)