University of Tennessee, Knoxville
Ayres Hall 208
1403 Circle Dr.
Knoxville, TN 37996
Broadly speaking, I analyze mathematical models that possess variational structures.
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." To appear in SIAM/ASA Journal on Uncertainty Quantification. A version with supplementary material is located here.
- T. Mengesha and J. Scott, "Strong Solvability for a Class of Nonlocal Systems of Equations Related to Peridynamics Using Fourier Analysis." In preparation.
- J. Scott and T. Mengesha, "A Fractional Korn-Type Inequality on Bounded Domains and Applications." In preparation.
Teaching (Spring 2019)
Math 141 Canvas Website