We present some results on the blow-up phenomenon for the Schrödinger equation in dimension three with a nonlinear term supported in a fixed point. We find sufficient conditions for the blow-up exploiting the moment of inertia of the solution and the uncertainty principle. In the critical case, we discuss the additional symmetries of the equation and construct a family of explicit blow-up solutions.
Blow up solutions for the Schroedinger equation with a concentrated nonlinearity in dimension three / R., Adami; Dell'Antonio, Gianfausto; R., Figari; Teta, Alessandro. - In: ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE. - ISSN 0294-1449. - STAMPA. - 21:1(2004), pp. 121-137. [10.1016/j.anihpc.2003.01.002]
Blow up solutions for the Schroedinger equation with a concentrated nonlinearity in dimension three.
DELL'ANTONIO, Gianfausto;TETA, Alessandro
2004
Abstract
We present some results on the blow-up phenomenon for the Schrödinger equation in dimension three with a nonlinear term supported in a fixed point. We find sufficient conditions for the blow-up exploiting the moment of inertia of the solution and the uncertainty principle. In the critical case, we discuss the additional symmetries of the equation and construct a family of explicit blow-up solutions.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
