The high exponent limit<i>p</i>→∞ for the one-dimensional nonlinear wave equation

Abstract

We investigate the behaviour of solutions φ = φ ( p) to the one-dimensional nonlinear wave equation, in the high exponent limit p → ∞ (holding φ 0 , φ 1 fixed).We show that if the initial data φ 0 , φ 1 are smooth with φ 0 taking values in (-1, 1) and obey a mild nondegeneracy condition, then φ converges locally uniformly to a piecewise limit φ (∞) taking values in the interval [-1, 1], which can in principle be computed explicitly.

Locations

• Analysis & PDE - View - PDF
• Project Euclid (Cornell University) - View - PDF
• Analysis & PDE - View - PDF
• Project Euclid (Cornell University) - View - PDF
• Analysis & PDE - View - PDF
• Project Euclid (Cornell University) - View - PDF