Asymptotic stability of traveling wave solutions for nonlocal viscous conservation laws with explicit decay rates

作者：Achleitner Franz^*; Ueda Yoshihiro

来源：Journal of Evolution Equations, 2018, 18(2): 923-946.

DOI：10.1007/s00028-018-0426-6

• Nonlocal evolution equations
• Riesz-Feller operator
• Fractional Laplacian
• Traveling wave solutions
• Asymptotic stability
• 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.

• 出版日期2018-6