@Article{JPDE-5-72,
author = {Fang Daoyuan},
title = {Nonlinear Superposition of Delta Waves in Multi-dimensional Space},
journal = {Journal of Partial Differential Equations},
year = {1992},
volume = {5},
number = {3},
pages = {72--84},
abstract = { We study the behavior of the solution u^&#949 to the semilinear wave equation with initial data a&#958 + u_i(i = 1, 2) in multidimensional space, where u_i is a classical function and a&#958 is smooth and converges to a distribution a_i as &#949 &#8594 0. In some circumstances one can prove the convergence of u^&#949, 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^&#949, delta wave, as the data become more singular is the sum of the two parts.},
issn = {2079-732X},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/jpde/5746.html}
}