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| THE CAUCHY PROBLEMS FOR DISSIPATIVE HYPERBOLIC MEAN CURVATURE FLOW |
| Shixia Lv,Zenggui Wang |
| (School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, Shandong, PR China) |
| DOI： |
| Abstract: |
| In this paper, we investigate initial value problems for hyperbolic mean curvature flow with a dissipative term. By means of support functions of a convex curve, a hyperbolic Monge-Ampère equation is derived, and this equation could be reduced to the first order quasilinear systems in Riemann invariants. Using the theory of the local solutions of Cauchy problems for quasilinear hyperbolic systems, we discuss lower bounds on life-span of classical solutions to Cauchy problems for dissipative hyperbolic mean curvature flow. |
| Key words: dissipative hyperbolic mean curvature flow; hyperbolic Monge-Ampère equation; lifespan |