Asymptotic behavior of solutions to conservation laws with diffusion-type terms of regularity-gain and regularity-loss

作者：Wang, Wenjun^*

来源：Journal of Mathematical Analysis and Applications, 2013, 400(2): 635-650.

DOI：10.1016/j.jmaa.2012.11.020

• Scalar conservation laws
• Weak dissipation
• Green function
• Optimal time-decay rates
• Pointwise estimate

In this paper, we study asymptotic behaviors of solutions to the Cauchy problem of nonlinear conservation laws with a diffusion-type source term related to an index s is an element of R. For s <= 1 and s > 1, the diffusion-type term takes on a characteristic of regularity-gain and regularity-loss on the high frequency domain, respectively. By combining the Green function method with the energy method, we overcome the weakly dissipative structure of the equation for the case of s > 1 and obtain the global existence and optimal L-p-norm time-decay rates of solutions. In the case of regularity-gain, pointwise estimates of solutions are shown by using the refined analysis on the Green function.

• 出版日期2013-4-15
• 单位上海理工大学