- Office: Manchester 387
- Home Page: https://holmesj.sites.wfu.edu/
- Email: holmesj 'at' wfu.edu
- BA, Wabash College, 2009
- MS University of Notre Dame 2010
- MS University of Notre Dame 2013
- PhD University of Notre Dame 2015
The analysis of partial differential equations, studying fundamental questions like existence and uniqueness of solutions, stability, and regularity properties
- J. Holmes and R. Puri, Non-uniqueness for the ab-family of equations, Journal of Mathematical Analysis and Applications, 493, 2021.
- J. Holmes and F. Tiglay, Non-uniform dependence of the data-to-solution map for the Hunter-Saxton equation in Besov spaces, Journal of Evolution Equations 18, 2018, 1173-1187.
- J. Holmes and F. Tiglay, Continuity properties of the solution map for the Euler-Poisson equation, Journal of Mathematical Fluid Mechanics 20, 2018, 757-769.
- J. Holmes, B. Keyfitz and F. Tiglay, Nonuniform dependence on initial data for compressible gas dynamics: The Cauchy problem on R2, SIAM Journal on Mathematical Analysis 50, 2018, 1237-1254. 5. J.
- Holmes and R. Thompson, Well-posedness and continuity properties of the Fornberg-Whitham equation in Besov spaces, Journal of Differential Equations, 263, 2017, 4355-4381.
- J. Holmes, Well–posedness and regularity of the generalized Burgers equation in periodic Gevrey spaces,Journal of Mathematical Analysis and Applications, 454, 2017, 18-40.
- J. Holmes and R. Thompson, Classical solutions of the generalized Camassa-Holm equation, Advancesin Differential Equations, 22, 2016, 339-362.
- J. Holmes, Well–posedness of the Fornberg-Whitham equation on the circle, Journal of Differential Equations, 260, 2016, 8530-8549.
- J. Holmes, Continuity properties of the data-to-solution map for the generalized Camassa-Holm equation, Journal of Mathematical Analysis and Applications. 417, 2014, 635-642.
- A. Himonas and J. Holmes, H ̈older continuity of the solution map for the Novikov equation, Journal of Mathematical Physics 54, 2013, 1-11.
- M. Axtell, J. Stickles and W. Trampbachls Zero-divisor ideals and realizable zero-divisor graphs, Involve 2 2009, 17-27.
- J. Holmes and A. Shull, Properties of Ideal Divisors, Pi Mu Epsilon Journal, 13 2009, 33-36.
MST 112, MST 113, MST 311, MST 383/683 - Stochastic calculus for financial mathematics.
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