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Multidimensional Oscillations for Non-linear Hyperbolic Mixed Problem: The Justified Non-linear Geometric Optics Method (1996)

Łada, A.

Chichester, West Sussex : Wiley-Blackwell

Mathematical Methods in the Applied Sciences 19 (1996), S. 217-233

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ISSN: 0170-4214

Keywords: Engineering ; Numerical Methods and Modeling

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Mathematics

Notes: The mixed-Neumann problem for the non-linear wave equation □u-a(u)(∣∂tu)∣2-∣∇u∣2 = fε(z) is studied. The function fε(z) = ∑k∊Kfk(z,ε-1φk(z),ε), ε∊[0,1], K is finite, fk(z,θk,ε) are 2π-periodic with respect to θk. The existence of solution uε on a domain z = (t,x,y)∊[0,T]×∝+×∝d, d = 1 or 2, is proved when ε is sufficiently small; T does not depend on ε. By the non-linear geometric optics method the asymptotic (with respect to ε→0) solution ũ ε is constructed. The estimation for the rest ε2rε = uε-ũε is derived and the limit rε, ε→0, is studied.

Type of Medium: Electronic Resource

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