Well-posedness and long-time behavior of Lipschitz solutions to extremal surface equations

Details Well-posedness and long-time behavior of Lipschitz solutions to extremal surface equations Well-posedness and long-time behavior of Lipschitz solutions to extremal surface equations

2010-10-21

arxiv.org/abs/1010.4403v2

Physics

Mathematical Physics

This paper has been withdrawn by the author due to a crucial error in Lemma 3.2

Scientific paper

We show that in one space dimension Lipschitz solutions of extremal surface equations are equivalent to entropy solutions in $L^\infty(\R)$ of a non-strictly hyperbolic system of conservation laws. We obtain an explicit representation formula and the uniqueness of the entropy solutions to the Cauchy problem of the system. By using this formula, we also obtain the convergence and convergence rates as $t \rightarrow +\infty$ of the entropy solutions to explicit traveling waves in the $L^1(\R)$ norm. Moreover, when initial data are constants outside of a finite space interval, the entropy solutions become the explicit traveling waves after a finite time. Finally, we prove $L^1$ stabilities of the entropy solutions.

Affiliated with

Also associated with

No associations

Rating

Well-posedness and long-time behavior of Lipschitz solutions to extremal surface equations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Well-posedness and long-time behavior of Lipschitz solutions to extremal surface equations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Well-posedness and long-time behavior of Lipschitz solutions to extremal surface equations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-423135