Geodesic
Blow-up of solutions of Cauchy problem for nonlinear Schr\"odinger equation
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2013), pp. 159-171

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In this work we study the effect of time finiteness of the existence of Cauchy problem for nonlinear Schrödinger equation solution. Together with the ill-posed Cauchy problem we consider its neighborhood in the space of operators, representing Cauchy problem. We explore the convergence of sequence of solutions of Cauchy problems with the operators, approximating the initial Hamiltonian.
Keywords: nonlinear Schrödinger equation, regularization, blow-up regime, blow-up of solution, viscosity solution. 
@article{VSGTU_2013_1_a14,
     author = {V. Zh. Sakbaev},
     title = {Blow-up of solutions of {Cauchy} problem for nonlinear {Schr\"odinger} equation},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {159--171},
     publisher = {mathdoc},
     number = {1},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2013_1_a14/}
}
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V. Zh. Sakbaev. Blow-up of solutions of Cauchy problem for nonlinear Schr\"odinger equation. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2013), pp. 159-171. http://geodesic.mathdoc.fr/item/VSGTU_2013_1_a14/