Non-oriented solutions of the eikonal equation
نویسندگان
چکیده
منابع مشابه
Non-oriented solutions of the eikonal equation
We study a new formulation for the eikonal equation |∇u| = 1 on a bounded subset of R. Instead of a vector field ∇u, we consider a field P of orthogonal projections on 1-dimensional subspaces, with divP ∈ L. We prove existence and uniqueness for solutions of the equation P divP = 0. We give a geometric description, comparable with the classical case, and we prove that such solutions exist only ...
متن کاملPartial Differential Equations Non-oriented Solutions of the Eikonal Equation
We study a new formulation for the eikonal equation |∇u| = 1 on a bounded subset of R. Instead of a vector field ∇u, we consider a field P of orthogonal projections on 1-dimensional subspaces, with div P ∈ L. We prove that solutions of this equation propagate direction as in the classical eikonal equation. We also show that solutions exist if and only if the domain is a tubular neighbourhood of...
متن کاملWavefronts and solutions of the eikonal equation
S U M M A R Y In this paper, several methods for the solution of the eikonal equation are investigated. Using the method of characteristics, traveltimes are computed along rays. Approximate solutions of the eikonal equation can also be obtained. From Fermat’s principle, first-order changes in the traveltime can be found by integrating along initial ray trajectories. Alternatively, linearized ra...
متن کاملHopf maps as static solutions of the complex eikonal equation
We demonstrate that a class of torus-shaped Hopf maps with arbitrary linking number obeys the static complex eikonal equation. Further , we explore the geometric structure behind these solutions, explaining thereby the reason for their existence. As this equation shows up as an integrability condition in certain non-linear field theories, the existence of such solutions is of some interest.
متن کاملEfficient traveltime solutions of the acoustic TI eikonal equation
Article history: Received 19 November 2013 Received in revised form 22 June 2014 Accepted 6 November 2014 Available online 13 November 2014
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Comptes Rendus Mathematique
سال: 2010
ISSN: 1631-073X
DOI: 10.1016/j.crma.2010.09.011