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Dr. John Holmes

Assistant Professor

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Dr. Holmes’s

  • Office: Manchester 387
  • Phone:
  • 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
Professional Website

 
  1. J. Holmes and R. Puri, Non-uniqueness for the ab-family of equations, Journal of Mathematical Analysis and Applications, 493, 2021.
  2.  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.
  3.  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.
  4.  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.
  5. 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.
  6. 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.
  7. J. Holmes and R. Thompson, Classical solutions of the generalized Camassa-Holm equation, Advancesin Differential Equations, 22, 2016, 339-362.
  8. J. Holmes, Well–posedness of the Fornberg-Whitham equation on the circle, Journal of Differential Equations, 260, 2016, 8530-8549.
  9. 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.
  10. A. Himonas and J. Holmes, H ̈older continuity of the solution map for the Novikov equation, Journal of Mathematical Physics 54, 2013, 1-11.
  11. M. Axtell, J. Stickles and W. Trampbachls Zero-divisor ideals and realizable zero-divisor graphs, Involve 2 2009, 17-27.
  12. 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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