Geodesic
Blow-up of solutions of an abstract Cauchy problem for a~formally hyperbolic equation with double non-linearity
Izvestiya. Mathematics , Tome 78 (2014) no. 5, pp. 937-985

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We consider an abstract Cauchy problem for a formally hyperbolic equation with double non-linearity. Under certain conditions on the operators in the equation, we prove its local (in time) solubility and give sufficient conditions for finite-time blow-up of solutions of the corresponding abstract Cauchy problem. The proof uses a modification of a method of Levine. We give examples of Cauchy problems and initial-boundary value problems for concrete non-linear equations of mathematical physics.
Keywords: finite-time blow-up, generalized Klein–Gordon equations, non-linear hyperbolic equations, non-linear mixed boundary-value problems, field theory. 
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     author = {M. O. Korpusov and A. A. Panin},
     title = {Blow-up of solutions of an abstract {Cauchy} problem for a~formally hyperbolic equation with double non-linearity},
     journal = {Izvestiya. Mathematics },
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     url = {http://geodesic.mathdoc.fr/item/IM2_2014_78_5_a4/}
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M. O. Korpusov; A. A. Panin. Blow-up of solutions of an abstract Cauchy problem for a~formally hyperbolic equation with double non-linearity. Izvestiya. Mathematics , Tome 78 (2014) no. 5, pp. 937-985. http://geodesic.mathdoc.fr/item/IM2_2014_78_5_a4/