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math.AP2012★ 6 cited
A computational method for the Helmholtz equation in unbounded domains based on the minimization of an integral functional
Giulio Ciraolo, Francesco Gargano, Vincenzo Sciacca
We study a new approach to the problem of transparent boundary conditions for the Helmholtz equation in unbounded domains. Our approach is based on the minimization of an integral…
math.AP2012★ 18 cited
Analytic solutions and Singularity formation for the Peakon b--Family equations
Giuseppe Maria Coclite, Francesco Gargano, Vincenzo Sciacca
Using the Abstract Cauchy-Kowalewski Theorem we prove that the -family equation admits, locally in time, a unique analytic solution. Moreover, if the initial data is real analyt…