Communications in Information and Systems

Volume 13 (2013)

Number 3

Special Issue in Honor of Marshall Slemrod: Part 3 of 4

Constructing completely integrable fields by a generalized-streamlines method

Pages: 327 – 355

DOI: https://dx.doi.org/10.4310/CIS.2013.v13.n3.a3

Authors

Antonella Marini (Dipartimento di Matematica, Università di L’Aquila, Italy; Department of Mathematical Sciences, Yeshiva University, New York, N.Y., U.S.A.)

Thomas H. Otway (Department of Mathematical Sciences, Yeshiva University, New York, N.Y., U.S.A.)

Abstract

The classical approach to visualizing a flow, in terms of its streamlines, motivates a topological/soft-analytic argument for constrained variational equations. In its full generality, that argument provides an explicit formula for completely integrable solutions to a broad class of $n$-dimensional quasilinear exterior systems. In particular, it yields explicit solutions for extremal surfaces in Minkowski space and for Born-Infeld models.

Keywords

Hodge-Frobenius equation, Born-Infeld model, completely integrable system, quasilinear system, elliptic-hyperbolic equation

2010 Mathematics Subject Classification

35M10, 35Q35

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Published 3 June 2014