Blake Barker

Assistant Professor of Mathematics

Brigham Young University

CV


ACME Advising



Scientific Software



Publications


  1. Euler vs. Lagrange: The role of coordinates in practical Evans-function computations, submitted, arXiv: 1707.01938, 2017 (with Jeffrey Humpherys, Gregory Lyng, and Kevin Zumbrun).
  2. Evans function computation for the stability of travelling waves, Phil. Trans. R. Soc. A 376: 20170184. http://dx.doi.org/10.1098/rsta.2017.0184 (with Jeffrey Humpherys, Joshua Lytle, and Gregory Lyng).
  3. Computing Evans functions numerically via boundary-value problems, Physica D: Nonlinear Phenomena, Vol 367, 1 - 10, 2018. DOI: https://doi.org/10.1016/j.physd.2017.12.002 (with Rose Nguyen, Börn Sandstede, Nathan Ventura, Colin Wahl).
  4. Balanced flux formulations for multidimensional Evans function computations for viscous shocks, Quart. Appl. Math. October 25, 2017. DOI: https://doi.org/10.1090/qam/1492.
  5. Turing patterns in parabolic systems of conservation laws and numerically observed stability of periodic waves, Physica D: Nonlinear Phenomena, Vol 367, 11-18, 2018. DOI: https://doi.org/10.1016/j.physd.2017.12.003. (with Soyeun Jung and Kevin Zumbrun).
  6. Note on the stability of viscous roll-waves, Comptes rendus Mecanique, Dec 2016, DOI:10.1016/j.crme.2016.11.001 (with Mathew Johnson, Pascal Noble, L. Miguel Rodrigues, and Kevin Zumbrun).
  7. Numerical proof of stability of isentropic Navier-Stokes shocks. Mathematical Models and Methods in Applied Sciences, Vol 26, No. 13. 2451-2469, 2016. (with Kevin Zumbrun).
  8. Stability of Viscous St. Venant Roll Waves: From Onset to Infinite Froude Number Limit Journal of Nonlinear Science, 1-58, 2016. DOI: 10.1007/s00332-016-9333-6 (with Mathew Johnson, Pascal Noble, L. Miguel Rodrigues, and Kevin Zumbrun).
  9. Viscous hyperstabilization of detonation waves in one space dimension, SIAM Journal on Applied Mathematics, 2015, 75(3): 885-906, (with Jeffrey Humpherys, Gregory Lyng, and Kevin Zumbrun).
  10. Convex entropy, Hopf bifurcation, and viscous and inviscid shock stability, Arch. Rational Mech. Anal., 2015 (DOI) 10.1007/s00205-014-0838-6, (with Heinrich Freistühler and Kevin Zumbrun).
  11. Numerical proof of stability of roll waves in the small-amplitude limit for inclined thin film flow, Journal of Differential Equations, 257: 2950-2983, 2014.
  12. Nonlinear Modulational Stability of Periodic Traveling-Wave Solutions of the Generalized Kuramoto-Sivashinsky Equation, Physica D, 258 no. 1: 11-46, 2013, (with Mathew Johnson, Pascal Noble, L. Miguel Rodrigues, and Kevin Zumbrun).
  13. Stability of periodic Kuramoto-Sivashinsky waves, Applied Mathematics Letters, 25 no. 5: 824-829, 2012, (with Mathew Johnson, Pascal Noble, L. Miguel Rodrigues, and Kevin Zumbrun).
  14. Existence and stability of viscoelastic shock profiles, Arch. Ration. Mech. Anal., Volume 200, Number 2, (2011) 491-532, (with Marta Lewicka and Kevin Zumbrun).
  15. Metastability of solitary roll wave solutions of the St. Venant equations with viscosity, Physica D, 240 (2011) no. 16: 1289-1310, (with Mathew Johnson, L. Miguel Rodrigues, and Kevin Zumbrun).
  16. Existence and stability of steady states of a reaction convection diffusion equation modeling microtubule formation, J. Math. Biol., Volume 63, (2011) 459-492, (with Shantia Yarahmadian, Kevin Zumbrun, and Sidney L. Shaw).
  17. Whitham averaged equations and modulational stability of periodic solutions of hyperbolic-parabolic balance laws, Journes quations aux drives partielles (2010), Exp. No. 3, (with Mathew Johnson, Pascal Noble, L. Miguel Rodrigues, and Kevin Zumbrun).
  18. Existence and stability of viscous shock profiles for 2-D isentropic MHD with infinite electrical resistivity, Acta Mathematica Scientia, Volume 30, Number 2 Series B, (2010) 447-498, (with Olivier Lafitte and Kevin Zumbrun).
  19. One-dimensional stability of parallel shock layers in isentropic magnetohydrodynamics, Journal of Differential Equations, 249(9):2175-2213, 2010 (with Jeffrey Humpherys and Kevin Zumbrun).
  20. Stability of viscous shocks in isentropic gas dynamics Comm. Math. Phys. 281 (2008), no. 1, 231-249 (with Jeffrey Humpherys, Keith Rudd, and Kevin Zumbrun).
  21. Stability of isentropic Navier-Stokes shocks, Appl. Math. Lett. 21 (2008), no. 7, 742-747 (with Jeffrey Humpherys, Olivier Lafitte, Keith Rudd, and Kevin Zumbrun).

Other Publications



Teaching

Math 290