As well as the solutions constructed in [H. Pecher, Nonlinear small data scattering for the wave and Klein Gordon equation, Math. Z. 185 (2) (1984) 261 270] to the focusing NLW for small initial data and to the ones obtained in [C.
The trail pheromone update in each matrix considers only the solutions constructed by the ants in its neighborhood.
At the end of the iteration, the pheromone values are modified based on the quality of the solutions constructed by the ants.
These results should shed light on the convergence of the numerical solution constructed by the Lax-Friedrichs scheme for the single-shock solution of system of hyperbolic conservation laws.
In most of cases, even when (f = 0), the mild solution constructed in Theorem 2.1 does not satisfy equation (1.1).
Namely ((u_{M} x,t),v _{M} x,t))) the maximal solution constructed in Lemma 2.4 and ((widetilde{u} x,t),widetilde{v} x,t))).
The boundary value problem for this dynamics is obviously well-posed: any set of data at an instant yields a unique global solution, constructed by the method sketched above.
We discuss the convergence of the approximate solutions constructed in equation (12).
The construction of complex spherical waves can also be done using the CGO solutions constructed in [107].
The CGO solutions constructed in Theorem 1.3 have been applied to determine inclusions for Helmholtz equations in [84] and Maxwell's equations in [209] using the enclosure method [83, 84].
