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Volume 35, Issue 2
The Cauchy Problems for Dissipative Hyperbolic Mean Curvature Flow

Shixia Lv & Zenggui Wang

Ann. Appl. Math., 35 (2019), pp. 159-179.

Published online: 2020-08

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  • 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.

  • Keywords

dissipative hyperbolic mean curvature flow, hyperbolic Monge-Ampère equation, lifespan.

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COPYRIGHT: © Global Science Press

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@Article{AAM-35-159, author = {Lv , Shixia and Wang , Zenggui}, title = {The Cauchy Problems for Dissipative Hyperbolic Mean Curvature Flow}, journal = {Annals of Applied Mathematics}, year = {2020}, volume = {35}, number = {2}, pages = {159--179}, 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.

}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/aam/18075.html} }
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 -

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.

Lv , Shixia and Wang , Zenggui. (2020). The Cauchy Problems for Dissipative Hyperbolic Mean Curvature Flow. Annals of Applied Mathematics. 35 (2). 159-179. doi:
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