On the Rate of Convergence and Asymptotic Profile of Solutions to the Viscous Burgers Equation

نویسنده

  • YONG-JUNG KIM
چکیده

In this paper we control the first moment of the initial approximations and obtain the order of convergence and the asymptotic profile of a general solution by two explicit “canonical” approximations: a diffusive N-wave and a diffusion wave solution. The order of convergence of both approximations is O(t1/(2r)−3/2) in Lr norm, 1 ≤ r ≤ ∞, as t → ∞, which is faster than the well-known classical convergence order O(t1/(2r)−1/2) for the inviscid Burgers equations case. A further comparison between the convergence rates of these two approximations and a discussion of the metastability phenomenon of the Burgers equation are also included. The method devised here allows us to obtain convergence up to any order by introducing new canonical solutions and controlling higher moments of the initial approximation.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Periodic Wave Shock solutions of Burgers equations

In this paper we investigate the exact peroidic wave shock solutions of the Burgers equations. Our purpose is to describe the asymptotic behavior of the solution in the cauchy problem for viscid equation with small parametr ε and to discuss in particular the case of periodic wave shock. We show that the solution of this problem approaches the shock type solution for the cauchy problem of the in...

متن کامل

Optimal L1 Decay Rate to Diffusion Waves for the Hamer Model of Radiating Gases

We are concerned with the asymptotic behavior of the solutions of a simplified model describing the evolution of a radiating gas. More precisely, we shall prove the convergence of H solutions toward the classical diffusion wave of the viscous Burgers’ equation by means of entropy methods. The result is also endowed with the same L rate of convergence of that case.

متن کامل

Asymptotic behavior of a system of two difference equations of exponential form

In this paper, we study the boundedness and persistence of the solutions, the global stability of the unique positive equilibrium point and the rate of convergence of a solution that converges to the equilibrium $E=(bar{x}, bar{y})$ of the system of two difference equations of exponential form: begin{equation*} x_{n+1}=dfrac{a+e^{-(bx_n+cy_n)}}{d+bx_n+cy_n}, y_{n+1}=dfrac{a+e^{-(by_n+cx_n)}}{d+...

متن کامل

Entropy Dissipation and Wasserstein Metric Methods for the Viscous Burgers’ Equation: Convergence to Diffusive Waves

In this paper we study the large time behavior for the viscous Burgers’ equation with initial data in L(R). In particular, after a time dependent scaling, we provide the optimal rate of convergence in relative entropy and Wasserstein metric, towards an equilibrium state corresponding to a positive diffusive wave. The main tool in our analysis is the reduction of the rescaled Burgers’ equation t...

متن کامل

Decay estimates of solutions to the IBq equation

‎In this paper we focus on the Cauchy problem for the generalized‎ ‎IBq equation with damped term in $n$-dimensional space‎. ‎We establish the global existence and decay estimates of solution with $L^q(1leq qleq 2)$ initial value‎, ‎provided that the initial value is suitably small‎. ‎Moreover‎, ‎we also show that the solution is asymptotic to the solution $u_L$ to the corresponding linear equa...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2007