ASYMPTOTIC BEHAVIOR OF MULTIDIMENSIONAL SCALAR RELAXATION SHOCKS
نویسندگان
چکیده
منابع مشابه
Asymptotic Behavior of Multidimensional Scalar Relaxation Shocks
We establish pointwise bounds for the Green function and consequent linearized stability for multidimensional planar relaxation shocks of general relaxation systems whose equilibrium model is scalar, under the necessary assumption of spectral stability. Moreover, we obtain nonlinear L asymptotic behavior/sharp decay rate of perturbed weak shocks of general simultaneously symmetrizable relaxatio...
متن کاملAsymptotic Dynamics in Scalar Field Theory: Anomalous Relaxation
We analyze the dynamics of dissipation and relaxation in the unbroken and broken symmetry phases of scalar theory in the nonlinear regime for large initial energy densities, and after linear unstabilities (parametric or spinodal) are shut-off by the quantum backreaction. A new time scale emerges that separates the linear from the non-linear regimes. This scale is non-perturbative in the couplin...
متن کاملExistence of semilinear relaxation shocks
We establish existence with sharp rates of decay and distance from the Chapman– Enskog approximation of small-amplitude shock profiles of a class of semilinear relaxation systems including discrete velocity models obtained from Boltzmann and other kinetic equations. Our method of analysis is based on the macro–micro decomposition introduced by Liu and Yu for the study of Boltzmann profiles, but...
متن کاملNavier-Stokes regularization of multidimensional Euler shocks
We establish existence and stability of multidimensional shock fronts in the vanishing viscosity limit for a general class of conservation laws with “real”, or partially parabolic, viscosity including the Navier–Stokes equations of compressible gas dynamics with standard or van der Waals-type equation of state. More precisely, given a curved Lax shock solution u of the corresponding inviscid eq...
متن کاملWeak Stability of Nonuniformly Stable Multidimensional Shocks
The aim of this paper is to investigate the linear stability of multidimensional shock waves that violate the uniform stability condition derived by A. Majda. Two examples of such shock waves are studied: (1) planar Lax shocks in isentropic gas dynamics (2) phase transitions in an isothermal van der Waals fluid. In both cases we prove an energy estimate on the resulting linearized system. Speci...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Hyperbolic Differential Equations
سال: 2009
ISSN: 0219-8916,1793-6993
DOI: 10.1142/s0219891609001964