361 research outputs found
On convergence of solutions of fractal Burgers equation toward rarefaction waves
In the paper, the large time behavior of solutions of the Cauchy problem for
the one dimensional fractal Burgers equation with is studied. It is shown that if the
nondecreasing initial datum approaches the constant states ()
as , respectively, then the corresponding solution converges
toward the rarefaction wave, {\it i.e.} the unique entropy solution of the
Riemann problem for the nonviscous Burgers equation.Comment: 15 page
Asymptotic stability of traveling wave solutions for nonlocal viscous conservation laws with explicit decay rates
We consider scalar conservation laws with nonlocal diffusion of Riesz-Feller
type such as the fractal Burgers equation. The existence of traveling wave
solutions with monotone decreasing profile has been established recently (in
special cases). We show the local asymptotic stability of these traveling wave
solutions in a Sobolev space setting by constructing a Lyapunov functional.
Most importantly, we derive the algebraic-in-time decay of the norm of such
perturbations with explicit algebraic-in-time decay rates
Large-time Behavior of Solutions to the Inflow Problem of Full Compressible Navier-Stokes Equations
Large-time behavior of solutions to the inflow problem of full compressible
Navier-Stokes equations is investigated on the half line .
The wave structure which contains four waves: the transonic(or degenerate)
boundary layer solution, 1-rarefaction wave, viscous 2-contact wave and
3-rarefaction wave to the inflow problem is described and the asymptotic
stability of the superposition of the above four wave patterns to the inflow
problem of full compressible Navier-Stokes equations is proven under some
smallness conditions. The proof is given by the elementary energy analysis
based on the underlying wave structure. The main points in the proof are the
degeneracies of the transonic boundary layer solution and the wave interactions
in the superposition wave.Comment: 27 page
Large-time Behavior of Solutions to the Inflow Problem of Full Compressible Navier-Stokes Equations
Large-time behavior of solutions to the inflow problem of full compressible
Navier-Stokes equations is investigated on the half line .
The wave structure which contains four waves: the transonic(or degenerate)
boundary layer solution, 1-rarefaction wave, viscous 2-contact wave and
3-rarefaction wave to the inflow problem is described and the asymptotic
stability of the superposition of the above four wave patterns to the inflow
problem of full compressible Navier-Stokes equations is proven under some
smallness conditions. The proof is given by the elementary energy analysis
based on the underlying wave structure. The main points in the proof are the
degeneracies of the transonic boundary layer solution and the wave interactions
in the superposition wave.Comment: 27 page
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