Math Publications

Math Publications Math Publications

Comparison of coarsening dynamics for the Cahn--Hilliard and Burgers--Cahn--Hilliard equations, Preprint 2024, PDF Version
Oscillation theory and instability of nonlinear waves, to appear in Discrete and Continuous Dynamical Systems,, PDF Version
Renormalized oscillation theory for linear Hamiltonian systems on [0,1] via the Maslov index, J. Dynamics and Differential Equations 36 (2024) 535--575 (with A. Sukhtayev, Miami University). PDF Version
The Maslov index and spectral counts for linear Hamiltonian systems on R, J. Dynamics and Differential Equations 35 (2023) 1947--1991, PDF Version
Renormalized oscillation theory for regular linear non-Hamiltonian systems, Communications on Pure and Applied Analysis 21 (2022) 4311-4345, PDF Version
Renormalized oscillation theory for singular linear Hamiltonian systems, J. Functional Analysis 283 (2022), (with A. Sukhtayev, Miami University). PDF Version
Hormander's index and oscillation theory, Journal of Mathematical Analysis and Applications 500 (2021) 1-38, PDF Version

The Maslov and Morse indices for Sturm-Liouville systems on the half-line, Discrete and Continuous Dynamical Systems A 40(2) (2020) 983-1012 (with A. Sukhtayev, Miami University). PDF Version
The Maslov index and spectral counts for linear Hamiltonian systems on [0,1], Journal of Dynamics and Differential Equations 30 (2018) 1703-1729 (with S. Jung, Kongju National University and B. Kwon, Ulsan National Institute of Science and Technology) PDF Version
The Maslov and Morse indices for Schrodinger operators on R, Indiana University Mathematics Journal 67 (2018) 1765-1815. (with Y. Latushkin, University of Missouri) and A. Sukhtayev, Indiana University). PDF Version
Spectral analysis of θ-periodic Schrodinger operators and applications to periodic waves, J. Differential Equations 264 (2018) 2205-2241 (with S. Jung, Kongju National University) PDF Version
The Maslov index for Lagrangian pairs on R^{2n}, Journal of Mathematical Analysis and Applications 451 (2017), no. 2, 794–821 (with Y. Latushkin, University of Missouri) and A. Sukhtayev, Indiana University). PDF Version
Linear Stability for Transition Front Solutions in Multidimensional Cahn-Hilliard Systems, Journal of Dynamics and Differential Equations 29 (2017) 895--955. PDF Version
The Maslov and Morse indices for Schrodinger operators on [0, 1], J. Differential Equations 260 (2016) 4499-4549. (with A. Sukhtayev, Indiana University). PDF Version
Stability for Transition Front Solutions in Multidimensional Cahn-Hilliard Systems, J. Nonlinear Science 26 (2016) 619-661. PDF Version
Stability of transition front solutions in Cahn-Hilliard systems, proceedings of the Research Institute of Mathematical Sciences, RIMS Kokyuroku, no. 1985, Mathematical Analysis in Fluid and Gas Dynamics (2015) 20-41 (with B. Kwon, Ulsan National Institute of Science and Technology). PDF Version

Short-time existence theory toward stability for nonlinear parabolic systems, Journal of Evolution Equations 15 (2015) 403-456. PDF Version
Spectral analysis for transition front solutions in multidimensional Cahn-Hilliard systems, J. Differential equations 257 (2014) 3448-3465. PDF Version
Asymptotic stability analysis for transition front solutions in Cahn-Hilliard systems, Physica D 241 (2012), no. 14, 1193-1222 (with B. Kwon, Ulsan National Institute of Science and Technology). PDF Version
Asymptotic Lp stability for transition fronts in Cahn-Hilliard systems, J. Differential equations 252 (2012) 5814--5831 (with B. Kwon, Ulsan National Institute of Science and Technology). PDF Version
Spectral analysis for transition front solutions in Cahn-Hilliard systems, Discrete and Continuous Dynamical Systems A 32 (2012) 126--166, (with B. Kwon, Ulsan National Institute of Science and Technology). PDF Version
Spectral analysis for periodic solutions of the Cahn-Hilliard equation on R NoDEA Nonlinear Differential Equations and Applications 18 (2011) 1--26, PDF Version

Spectral analysis for stationary solutions of the Cahn--Hilliard equation in R^d Communications in Partial Differential Equations 35 (2010) 590--612, PDF Version
Spectral analysis of stationary solutions of the Cahn--Hilliard equation Advances in Differential Equations 14 (2009) 87--120, Journal Version.
Spectral analysis of planar transition fronts for the Cahn--Hilliard equation J. Differential Equations 245 (2008) 594--615, PDF Version
Asymptotic behavior near planar transition fronts for equations of Cahn--Hilliard type, Physica D 229 (2007) 123--165. View Abstract or PDF Version
Nonlinear stability of degenerate shock profiles Differential and Integral Equations 20 (2007) 515--560, View Abstract or Journal Version.
Asymptotic behavior near transition fronts for equations of generalized Cahn--Hilliard form Communications in Mathematical Physics 269 (2007) 765--808, View Abstract or PDF Version
Stability of undercompressive shocks, Hyperbolic problems: theory, numerics and applications. I, 155-162, Yokohama Publ., Yokohama, 2006. (with K. Zumbrun, Indiana University)
Pointwise asymptotic behavior of perturbed viscous shock profiles Advances in Differential Equations 11 (2006) 1031--1080. (with Mohammadreza Raoofi, Indiana University) View Abstract or Journal Version.
Sharp pointwise bounds for perturbed viscous shock waves J. Hyperbolic Differential Equations 3 (2006) 1--77. (with Mohammadreza Raoofi, Max Planck Institute for Mathematics in the Sciences, and K. Zumbrun, Indiana University) View Abstract or PDF Version
Stability of undercompressive shock profiles, J. Differential Equations 225 (2006) 308--360 (with K. Zumbrun, Indiana University) View Abstract or PDF Version
Nonlinear stability for multidimensional fourth order shock fronts, Arch. Rational Mech. Anal. 181 (2006) 201--260 (with C. Hu, U. Louisville). View Abstract or PDF Version
Pointwise Green's function estimates toward stability for degenerate viscous shock waves Communications in Partial Differential Equations 31 (2006) 73--121. View Abstract or PDF Version

Stability of undercompressive shock profiles, refereed proceedings in HYP2004: Proceedings of the Tenth International Conference on Hyperbolic Problems (2005) (with K. Zumbrun, Indiana University).
Pointwise Green's function estimates toward stability for multidimensional fourth order viscous shock fronts, J. Differential Equations 218 (2005) 325--389 (with C. Hu, U. Louisville). View Abstract or PDF Version
The Evans function and stability criteria for degenerate viscous shock waves (with K. Zumbrun, Indiana University) Discrete and Continuous Dynamical Systems 10 (2004) 837--855. View Abstract or PDF Version
Local tracking and stability for degenerate viscous shock waves J. Differential Equations 186 (2002) 440--469. View Abstract or PDF Version
Pointwise estimates and stability for degenerate viscous shock waves J. Reine Angew. Math. 545 (2002) 19--65. View Abstract or PDF Version

Pointwise estimates and stability for dispersive-diffusive shock waves (with K. Zumbrun, Indiana University), Arch. Rational Mech. Anal. 155 (2000) 85--169. View Abstract or PDF Version
Pointwise Green's function approach to stability for scalar conservation laws, Comm. Pure Appl. Math. 52 (1999), no. 10, 1295--1313. View Abstract or View PDF
Pointwise estimates on the Green's function for a scalar linear convection-diffusion equation, J. Differential Equations 155 (1999) 327--367. View Abstract or View PDF
Shift invariance of the Brownian Bridge process, (with K. Zumbrun, Indiana University) Stat. and Prob. Letters 45 (1999) 379-382. View Abstract or View PDF
Pointwise semigroup methods and stability of viscous shock waves (with K. Zumbrun, Indiana University) Indiana Univ. J. Math. 47(1998), no. 3, 741--871. View Abstract or PDF Version
Pointwise estimates for the stability for scalar conservation laws, Thesis at Indiana University, under the direction of K. Zumbrun, 1998.