Nonlinear stability of generalized Benjamin–Bona–Mahony–Burgers shock profiles in several dimensions
نویسندگان
چکیده
منابع مشابه
Nonlinear stability of degenerate shock profiles
We consider degenerate viscous shock profiles arising in systems of two regularized conservation laws, where degeneracy here describes viscous shock profiles for which the asymptotic endstates are sonic to the associated hyperbolic system (the shock speed is equal to one of the characteristic speeds). Proceeding with pointwise estimates on the Green’s function for the linear system of equations...
متن کاملSpectral stability of small-amplitude viscous shock waves in several space dimensions
A planar viscous shock profile of a hyperbolic-parabolic system of conservation laws is a steady solution in a moving coordinate frame. The asymptotic stability of viscous profiles and the related vanishing-viscosity limit are delicate questions already in the well understood case of one space dimension and even more so in the case of several space dimensions. It is a natural idea to study the ...
متن کاملStability of Scalar Radiative Shock Profiles
This work establishes nonlinear orbital asymptotic stability of scalar radiative shock profiles, namely, traveling wave solutions to the simplified model system of radiating gas [8], consisting of a scalar conservation law coupled with an elliptic equation for the radiation flux. The method is based on the derivation of pointwise Green function bounds and description of the linearized solution ...
متن کاملExistence and stability of viscoelastic shock profiles
We investigate existence and stability of viscoelastic shock profiles for a class of planar models including the incompressible shear case studied by Antman and MalekMadani. We establish that the resulting equations fall into the class of symmetrizable hyperbolic–parabolic systems, hence spectral stability implies linearized and nonlinear stability with sharp rates of decay. The new contributio...
متن کاملSpectral stability of weak relaxation shock profiles
Using a combination of Kawashimaand Goodman-type energy estimates, we establish spectral stability of general small-amplitude relaxation shocks of symmetric dissipative systems. This extends previous results obtained by Plaza and Zumbrun [9] by singular perturbation techniques under an additional technical assumption, namely, that the background equation be noncharacteristic with respect to the...
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 Mathematical Analysis and Applications
سال: 2013
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2013.04.054