2017 - SIAM Fellow For his contributions in traveling wave stability and his exceptional mentoring of graduate students and post-doctoral researchers.
2014 - Fellow of the American Mathematical Society For contributions to continuum mechanics, shock, and boundary layer theory.
Kevin Zumbrun mostly deals with Mathematical analysis, Shock wave, Pointwise, Function and Inviscid flow. His Mathematical analysis study combines topics from a wide range of disciplines, such as Classical mechanics, Shock and Linear stability. His studies in Shock wave integrate themes in fields like Compressibility, Boundary value problem and Instability.
His study in Pointwise is interdisciplinary in nature, drawing from both Hyperbolic partial differential equation and Special case. His work carried out in the field of Function brings together such families of science as Traveling wave, Essential spectrum and Euler equations. His Inviscid flow research is multidisciplinary, incorporating elements of Multiphase flow and Fluid mechanics.
His main research concerns Mathematical analysis, Conservation law, Shock wave, Function and Pointwise. The Operator research Kevin Zumbrun does as part of his general Mathematical analysis study is frequently linked to other disciplines of science, such as Viscosity, therefore creating a link between diverse domains of science. His Operator research integrates issues from Spectral gap and Spectrum.
His Conservation law research incorporates themes from Hyperbolic partial differential equation, Exponential stability, Stable manifold and Nonlinear stability. His Shock wave study combines topics in areas such as Instability, Navier–Stokes equations, Compressibility and Inviscid flow, Classical mechanics. His Pointwise research is multidisciplinary, incorporating perspectives in Semigroup, Scalar and Resolvent.
His scientific interests lie mostly in Mathematical analysis, Function, Inviscid flow, Shock and Boundary. His Mathematical analysis study often links to related topics such as Spectral stability. Kevin Zumbrun interconnects Operator and Bounded function in the investigation of issues within Function.
His Boundary study incorporates themes from Classical mechanics and Asymptotic analysis. His research integrates issues of Wake and Nonlinear stability in his study of Pointwise. While the research belongs to areas of Periodic boundary conditions, Kevin Zumbrun spends his time largely on the problem of Bifurcation, intersecting his research to questions surrounding Conservation law.
His primary scientific interests are in Mathematical analysis, Function, Inviscid flow, Shock and Boundary. In his works, Kevin Zumbrun undertakes multidisciplinary study on Mathematical analysis and Froude number. He combines subjects such as Exponential stability, Spectral gap, Boundary value problem, Operator and Bounded function with his study of Function.
His biological study spans a wide range of topics, including Ideal gas, Statistical mechanics, Euler's formula and Shock wave. Kevin Zumbrun focuses mostly in the field of Shock, narrowing it down to topics relating to Mechanics and, in certain cases, Asymptotic analysis and Eigenvalues and eigenvectors. The study incorporates disciplines such as Unit sphere, Ball, Domain and Surface in addition to Boundary.
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The gap lemma and geometric criteria for instability of viscous shock profiles
Robert A. Gardner;Kevin Zumbrun.
Communications on Pure and Applied Mathematics (1998)
Pointwise Semigroup Methods and Stability of Viscous Shock Waves
Kevin Zumbrun;Peter Howard.
Indiana University Mathematics Journal (1998)
Multi-dimensional diffusion waves for the Navier-Stokes equations of compressible flow
David Hoff;Kevin Zumbrun.
Indiana University Mathematics Journal (1995)
Pointwise decay estimates for multidimensional Navier-Stokes diffusion waves
David Hoff;Kevin Zumbrun.
Zeitschrift für Angewandte Mathematik und Physik (1997)
Multidimensional Stability of Planar Viscous Shock Waves
Viscous and inviscid stability of multidimensional planar shock fronts
K. Zumbrun;D. Serre.
Indiana University Mathematics Journal (1999)
Large Viscous Boundary Layers For Noncharacteristic Nonlinear Hyperbolic Problems
Guy Métivier;Kevin R. Zumbrun.
Connectivity of Phase Boundaries in Strictly Convex Domains
Peter Sternberg;Kevin Zumbrun.
Archive for Rational Mechanics and Analysis (1998)
Stability of Large-Amplitude Shock Waves of Compressible Navier–Stokes Equations
Kevin Zumbrun;Helge Kristian Jenssen;Gregory Lyng.
arXiv: Mathematical Physics (2005)
Analytically varying eigenvectors and the stability of viscous shock waves
Leon Brin;Kevin Zumbrun.
Matemática Contemporânea (2002)
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