We consider the sharp interface limit epsilon -> 0(+) of the semilinear wave equation square u + del W(u)/epsilon(2) = 0 in R(1+n), where u takes values in R(k), k = 1, 2, and W is a double-well potential if k = 1 and vanishes on the unit circle and is positive elsewhere if k = 2. For fixed epsilon > 0 we find some special solutions, constructed around minimal surfaces in R(n). In the general case, under some additional assumptions, we show that the solutions converge to a Radon measure supported on a time-like k-codimensional minimal submanifold of the Minkowski space-time. This result holds also after the appearance of singularities, and enforces the observation made by J. Neu that this semilinear equation can be regarded as an approximation of the Born-Infeld equation.
|Autori:||BELLETTINI G; NOVAGA M.; ORLANDI G|
|Titolo:||Time-like minimal submanifolds as singular limits of nonlinear wave equations|
|Anno del prodotto:||2010|
|Digital Object Identifier (DOI):||10.1016/j.physd.2009.12.004|
|Appare nelle tipologie:||1.1 Articolo in rivista|