Math Publications

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The following papers were partially supported by the National Science Foundation under grant DMS-0906370.

• Spectral analysis for periodic solutions of the Cahn-Hilliard equation on R Preprint 2009, PDF Version

The following papers were partially supported by the National Science Foundation under grant DMS-0500988.

• Spectral analysis for stationary solutions of the Cahn--Hilliard equation in R^d to appear in Communications in Partial Differential Equations, PDF Version
• Spectral analysis of stationary solutions of the Cahn--Hilliard equation Advances in Differential Equations 14 (2009) 87--120, PDF 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 PDF 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
• Pointwise asymptotic behavior of perturbed viscous shock profiles Advances in Differential Equations 9 (2006) 1031--1080. (with Mohammadreza Raoofi, Indiana University) View Abstract or PDF 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

The following papers were partially supported by the National Science Foundation under grant DMS-0230003.

• 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 Changbing Hu, Texas A&M University) 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
• Pointwise Green's function estimates toward stability for multidimensional fourth order viscous shock fronts, J. Differential Equations 218 (2005) 325--389 (with Changbing Hu, Texas A&M University) 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

The following papers were partially supported by the National Science Foundation under grant DMS-9804390.

• 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 Postscript 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

The following doctoral dissertation was partially supported by the National Science Foundation under grant DMS--9706842.

• Pointwise estimates for the stability for scalar conservation laws, Thesis at Indiana University, under the direction of K. Zumbrun, 1998.