This paper develops the basic analytical theory related to some recently intro- duced crowd dynamics models. Where well posedness was known only locally in time, it is here extended to all of R＋. The results on the s...This paper develops the basic analytical theory related to some recently intro- duced crowd dynamics models. Where well posedness was known only locally in time, it is here extended to all of R＋. The results on the stability with respect to the equations are improved. Moreover, here the case of several populations is considered, obtaining the well posedness of systems of multi-D non-local conservation laws. The basic analytical tools are provided by the classical Kruzkov theory of scalar conservation laws in several space dimensions.展开更多
In this paper the author devotes to studying a logarithmic type nonlocal plane curve flow.Along this flow,the convexity of evolving curve is preserved,the perimeter decreases,while the enclosed area expands.The flow i...In this paper the author devotes to studying a logarithmic type nonlocal plane curve flow.Along this flow,the convexity of evolving curve is preserved,the perimeter decreases,while the enclosed area expands.The flow is proved to exist globally and converge to a finite circle in the C∞metric as time goes to infinity.展开更多
基金supported by the GNAMPA 2011 project Non Standard Applications of Conservation Laws
文摘This paper develops the basic analytical theory related to some recently intro- duced crowd dynamics models. Where well posedness was known only locally in time, it is here extended to all of R＋. The results on the stability with respect to the equations are improved. Moreover, here the case of several populations is considered, obtaining the well posedness of systems of multi-D non-local conservation laws. The basic analytical tools are provided by the classical Kruzkov theory of scalar conservation laws in several space dimensions.
基金supported by the National Natural Science Foundation of China(No.41671409)。
文摘In this paper the author devotes to studying a logarithmic type nonlocal plane curve flow.Along this flow,the convexity of evolving curve is preserved,the perimeter decreases,while the enclosed area expands.The flow is proved to exist globally and converge to a finite circle in the C∞metric as time goes to infinity.
