Volume 5, Issue 3
Nonlinear Superposition of Delta Waves in Multi-dimensional Space

Fang Daoyuan

J. Part. Diff. Eq.,5(1992),pp.72-84

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  • Abstract

We study the behavior of the solution u^ε to the semilinear wave equation with initial data aξ + u_i(i = 1, 2) in multidimensional space, where u_i is a classical function and aξ is smooth and converges to a distribution a_i as ε → 0. In some circumstances one can prove the convergence of u^ε, and our results express a striking superposition principle. The singular part of the solution propagates linearly. The classical part shows the nonlinear effects. And, the limit of the nonlinear solution u^ε, delta wave, as the data become more singular is the sum of the two parts.

  • History

Published online: 1992-05

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