Geodesic
Blow-Up of the Solution of an Inhomogeneous System of Sobolev-Type Equations
Matematičeskie zametki, Tome 91 (2012) no. 2, pp. 225-239

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We consider a model system of two inhomogeneous nonlinear Sobolev-type equations of sixth order with second-order time derivative and prove the local (with respect to time) solvability of the problem. We state conditions under which the blow-up of the solution occurs in finite time and find an upper bound for the blow-up time.
Keywords: system of Sobolev-type equations, blow-up of solutions, blow-up time, ion-sound wave, locally Lipschitz operator, Banach space, Friedrichs inequality. 
@article{MZM_2012_91_2_a5,
     author = {Yu. V. Mukhartova and A. A. Panin},
     title = {Blow-Up of the {Solution} of an {Inhomogeneous} {System} of {Sobolev-Type} {Equations}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {225--239},
     publisher = {mathdoc},
     volume = {91},
     number = {2},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_91_2_a5/}
}
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Yu. V. Mukhartova; A. A. Panin. Blow-Up of the Solution of an Inhomogeneous System of Sobolev-Type Equations. Matematičeskie zametki, Tome 91 (2012) no. 2, pp. 225-239. http://geodesic.mathdoc.fr/item/MZM_2012_91_2_a5/