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The Cauchy Problem for the Nonlinear Long Longitudinal Waves Equation in a Viscoelastic Rod |
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| Authors: | Umarov Kh. G. |
| Affiliation: | 1.Academy of Sciences of the Chechen Republic, Grozny, Russia ;2.Chechen State Pedagogical University, Grozny, Russia ; |
| Abstract: | We study the Cauchy problem in the space of continuous functionsfor some nonlinear differential equation of Sobolev type that simulates longitudinal waves in an infinite viscoelastic rod.Under consideration are the conditions for the existence of the global classical solution and the blow-upof the solution to the Cauchy problem on a finite time interval. |
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