On the system of Hamilton-Jacobi and transport equations arising in geometrical optics

Ben Moussa B.; Kossioris GT.

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On the system of Hamilton-Jacobi and transport equations arising in geometrical optics

机译：关于Hamilton-Jacobi系统和几何光学中的输运方程

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In the present article, we study the system of eikonal and transport equations arising in geometrical optics. The mathematical analysis is performed by using the suitable notion of solution, i.e., the viscosity solution for the Hamilton-Jacobi equation and the measure solution for the transport equation defined via the generalized Filippov characteristics. We Study the stability as well as the geometry of the solution to the system. [References: 42]

机译：在本文中，我们研究几何光学中产生的本征方程和输运方程。通过使用适当的溶液概念，即汉密尔顿-雅各比方程的粘度溶液和通过广义Filippov特性定义的运输方程的度量溶液，来进行数学分析。我们研究系统解的稳定性以及几何形状。 [参考：42]

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《Communications in Partial Differential Equations》 |2003年第6期|共27页
作者
Ben Moussa B.; Kossioris GT.;
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正文语种 eng
中图分类偏微分方程;
关键词
High frequency asymptotics; Wkb approximation; Paraxial approximation; Eikonal equation; Transport equation; Viscosity solutions; Measure solutions; Caustics; Singularities; Multivalued solutions; Blow-up; Partial-differential equations; Viscosity solutions; Eikonal equation; Computation; Approximations; Singularities; Convergence;

机译：高频渐近;Wkb近似;近轴近似;Eikonal方程;运输方程;粘度解;测量解;焦散;奇异性;多值解;爆破;偏微分方程;粘度解;Eikonal方程;计算;近似;奇异性;收敛;

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1. On the system of Hamilton-Jacobi and transport equations arising in geometrical optics [J] . Ben Moussa B., Kossioris GT. Communications in Partial Differential Equations . 2003,第5a6期

机译：关于Hamilton-Jacobi系统和几何光学中的输运方程
2. On a monge-ampere equation arising in geometric optics [J] . Pengfei Guan, Xu-Jia Wang Journal of Differential Geometry . 1998,第2期

机译：关于几何光学中产生的单安培方程
3. Some algebro-geometric solutions for the coupled modified Kadomtsev-Petviashvili equations arising from the Neumann type systems [J] . Chen J. Journal of Mathematical Physics . 2012,第7期

机译：由Neumann型系统产生的耦合修改的Kadomtsev-Petviashvili方程的一些代数几何解
4. Transport Rays and Applications to Hamilton-Jacobi Equations [C] . Stefano Bianchini, Matteo Gloyer C.I.M.E. School . 2011

机译：将光线和应用运输到哈密尔顿 - 雅各比方程
5. Numerical solutions of the Hamilton-Jacobi equations arising in nonlinear H(infinity) and optimal control. [D] . Markman, Jerry. 1998

机译：非线性H（无穷大）中的Hamilton-Jacobi方程的数值解和最优控制。
6. Effective 1D Time-Dependent Schrödinger Equations for 3D Geometrically Correlated Systems [O] . Devashish Pandey, Xavier Oriols, Guillermo Albareda 2020

机译：用于3D几何相关系统的有效的1D时间依赖性Schrödinger方程
7. On a numerical minimization problem for a new class of nonlinear partial differential equations arising in nonspherical geometrical optics and beamforming lenticular antennas II [O] . Sternberg Robert L., Grafton Robert B. 1988

机译：非球面几何光学和波束成形双凸透镜天线中一类新的非线性偏微分方程的数值最小化问题

On the system of Hamilton-Jacobi and transport equations arising in geometrical optics

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