TY - JOUR
T1 - The Cauchy Problems for Dissipative Hyperbolic Mean Curvature Flow
AU - Lv , Shixia
AU - Wang , Zenggui
JO - Annals of Applied Mathematics
VL - 2
SP - 159
EP - 179
PY - 2020
DA - 2020/08
SN - 35
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/aam/18075.html
KW - dissipative hyperbolic mean curvature flow, hyperbolic Monge-Ampère equation, lifespan.
AB - <p style="text-align: justify;">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.<br/></p>