Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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A remark on the existence of global BV solutions for a nonlinear hyperbolic wave equation


Authors: João-Paulo Dias and Mário Figueira
Journal: Quart. Appl. Math. 60 (2002), 245-250
MSC: Primary 35L70; Secondary 35D05
DOI: https://doi.org/10.1090/qam/1900492
MathSciNet review: MR1900492
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Abstract: By means of a suitable change of variables we obtain, by application of a general result by Dafermos and Hsiao, cf. [2], an existence theorem in $ {L^\infty } \cap {BV_{loc}}$ of a weak solution of the system corresponding to the quasilinear hyperbolic equation

$\displaystyle {\phi _{tt}} - p'\left( {\phi _x} \right){\phi _{xx}} + {\phi _t}... ...\qquad in \qquad \mathbb{R} \times \left[ {0, + \infty } \left[ \right. \right.$

, for small initial data in BV. This theorem is a partial extension of Dafermos's result for the case with $ F\left( \phi \right) \equiv 0$, proved in [1].

References [Enhancements On Off] (What's this?)

  • [1] C. M. Dafermos, A system of hyperbolic conservation laws with frictional damping, Z. Angew. Math. Phys. 46 (1995), no. Special Issue, S294–S307. Theoretical, experimental, and numerical contributions to the mechanics of fluids and solids. MR 1359325
  • [2] C. M. Dafermos and L. Hsiao, Hyperbolic systems and balance laws with inhomogeneity and dissipation, Indiana Univ. Math. J. 31 (1982), no. 4, 471–491. MR 662914, https://doi.org/10.1512/iumj.1982.31.31039
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DOI: https://doi.org/10.1090/qam/1900492
Article copyright: © Copyright 2002 American Mathematical Society


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