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Title of Journal: J Dyn Diff Equat

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Abbravation: Journal of Dynamics and Differential Equations

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Springer US

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DOI

10.1002/ctpp.19850250209

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1572-9222

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Eigenvalues of SelfSimilar Solutions of the Dafer

Authors: Stephen Schecter
Publish Date: 2006/03/03
Volume: 18, Issue: 1, Pages: 53-101
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Abstract

The Dafermos regularization of a system of n conservation laws in one space dimension admits smooth selfsimilar solutions of the form u=uX/T In particular there are such solutions near a Riemann solution consisting of n possibly large Lax shocks In Lin and Schecter 2004 SIAM J Math Anal 35 884–921 eigenvalues and eigenfunctions of the linearized Dafermos operator at such a solution were studied using asymptotic expansions Here we show that the asymptotic expansions correspond to true eigenvalue–eigenfunction pairs The proofs use geometric singular perturbation theory in particular an extension of the Exchange Lemma

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Other Papers In This Journal:
  1. Basic Reproduction Ratios for Periodic Compartmental Models with Time Delay
  2. A Grobman–Hartman Theorem for Control Systems
  3. Invariant Tori of Full Dimension for Second KdV Equations with the External Parameters
  4. Second Order Abstract Neutral Functional Differential Equations
  5. Complete Global and Bifurcation Analysis of a Stoichiometric Predator–Prey Model
  6. Existence of Rotating Spots with Spatially Dependent Feedback in the Plane in a Wave Front Interaction Model
  7. A Permutation Related to Non-compact Global Attractors for Slowly Non-dissipative Systems
  8. Random Attractor Associated with the Quasi-Geostrophic Equation
  9. Existence and Asymptotic Behavior of Solutions to Semilinear Wave Equations with Nonlinear Damping and Dynamical Boundary Condition
  10. A Free Boundary Problem for the Predator–Prey Model with Double Free Boundaries
  11. Stability of Solitary Waves for the Generalized Higher-Order Boussinesq Equation
  12. A Few Remarks on Partially Hyperbolic Diffeomorphisms of $${\mathbb T}^3$$ Isotopic to Anosov
  13. On The Number of Characteristic Lines for Homogeneous Vector Fields
  14. Real Analytic Quasi-Periodic Solutions with More Diophantine Frequencies for Perturbed KdV Equations
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