Academic Communication

Global Large Solutions to a Viscous Heat-Conducting One-Dimensional Gas with Temperature-Dependent Viscosity2015-12-04

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Speaker:Pro. Zhao Huijiang

Time:2015年12月4日 16:00—17:00

Location: Room 707, Teaching Building, 83 West Third Ring Road North, Haidian District, Beijing, 100089 China.

Organzier:School of Mathematical Sciences Capital Normal University

Introduction:In this talk, it is proved that the Cauchy problem of Rosenau equation is global well-posed for initial data in H^s(R)(s> 0), and ill-posed for initial data in H^s(R)(s < 0) in the sense that the flow mapping is not continuous at the origin from H^s(R) to D'(R) at any fixed t > 0 small enough. Moreover, it is showed that the solution to the Cauchy problem of Rosenau equation has unique continuation property under two sufficient conditions on initial data. On the other hand,  It is also proved that the initial boundary value problem has a unique global distributional solution, and the solution mapping is Lipschitz continuous in a neighborhood of initial data.