Geodesic
Blow-up and global solubility in the classical~sense of~the~Cauchy~problem~for~a~formally~hyperbolic~equation with a~non-coercive source
Izvestiya. Mathematics , Tome 84 (2020) no. 5, pp. 930-959

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We consider an abstract Cauchy problem with non-linear operator coefficients and prove the existence of a unique non-extendable classical solution. Under certain sufficient close-to-necessary conditions, we obtain finite-time blow-up conditions and upper and lower bounds for the blow-up time. Moreover, under certain sufficient close-to-necessary conditions, we obtain a result on the existence of a global-in-time solution independently of the size of the initial functions.
Keywords: non-linear Sobolev-type equations, blow-up, local solubility, non-linear capacity, bounds for the blow-up time. 
@article{IM2_2020_84_5_a4,
     author = {M. O. Korpusov},
     title = {Blow-up and global solubility in the classical~sense {of~the~Cauchy~problem~for~a~formally~hyperbolic~equation} with a~non-coercive source},
     journal = {Izvestiya. Mathematics },
     pages = {930--959},
     publisher = {mathdoc},
     volume = {84},
     number = {5},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2020_84_5_a4/}
}
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M. O. Korpusov. Blow-up and global solubility in the classical~sense of~the~Cauchy~problem~for~a~formally~hyperbolic~equation with a~non-coercive source. Izvestiya. Mathematics , Tome 84 (2020) no. 5, pp. 930-959. http://geodesic.mathdoc.fr/item/IM2_2020_84_5_a4/