Convergence to diffusion waves of the solutions for benjamin-bona-mahony-burgers equations

Abstract

This paper is concerned with the large-time behavior of solution of the Cauchy problem for the Benjamin-Bona-Mahony-Burgers equation. We prow that the solution unique globally exists and time-asymptotically tends to its corresponding diffusion wave, when the initial perturbation is small enough. The corresponding diffusion wave is constructed by the heat equation or the Burgers equation. In particular, we obtain the convergence rates in L^q-spaces (2≤q≤∞). The mathematical proof is based on the Fourier transform method and the energy method.Furthermore, we take the numerical computations on such a problem. The numerical simulations show that the convergence rates obtained theoretically seem to be sharp

Keywords:

• BBM-Burgers equations
• diffusion waves
• stability

AMS:

• 35453
• 35B40
• 76B15