Abstract
In this paper we prove the existence of the unique global classical solution with small initial data to the Cauchy problem of a scalar conservation law with degenerate diffusion by establishing the uniform a priori decay estimates of solutions. In order to compensate the degeneracy on the x1 direction by the diffusion on other directions, we introduce the frequency decomposition method and obtain the low frequency estimate and the high frequency estimate of the solution by the Green's function method and energy method respectively.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
