Nonlinear Superposition of Delta Waves in Multi-dimensional Space (Journal of Partial Differential Equations, 1992)
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.