On Global Solvability of One-Dimensional Quasilinear Wave Equations

Abstract

The paper concerns global solvability of initial value problem for one class of hyperbolic quasilinear second order equations with two independent variables, which have a rather wide range of applications. Besides existence and uniqueness of maximal solutions of this problem it is proved that a maximal solution possess the completeness property that is an analog of the corresponding property of ordinary differential equations. Namely, a solution of an ordinary differential equation that is defined on a maximal interval leaves any compact subset of the equation domain.

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Funding

This work was supported by the Russian Foundation for Basic Research (projects no. 19-51-50005 and 20-01-00610).

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Correspondence to D. V. Tunitsky.

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(Submitted by J. S. Krasil’shchik)

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Tunitsky, D.V. On Global Solvability of One-Dimensional Quasilinear Wave Equations. Lobachevskii J Math 41, 2510–2524 (2020). https://doi.org/10.1134/S1995080220120422

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Keywords:

  • hyperbolic quasilinear equations
  • initial value problem
  • multivalued solutions
  • characteristic uniformization