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On the existence of a generalized solution of a nonlinear evolution system of equations in a domain unbounded in time

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Abstract

We consider a mixed problem with Dirichlet homogeneous boundary conditions and nonzero initial conditions for a nonlinear coupled evolution system of equations in a domain unbounded in time. The conditions of existence of a generalized solution are obtained. It is shown that no solution of the problem exists at a negative initial value of the energy integral.

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Authors and Affiliations

  1. Mechanico-Mathematical Faculty, Ivan Franko Lviv National University, Lviv, 79000, Ukraine

    Maksim Nechepurenko & Galina Torgan

Authors
  1. Maksim Nechepurenko
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  2. Galina Torgan
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Correspondence to Maksim Nechepurenko.

Additional information

Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 7, No. 1, p. 49–72, January–February, 2010.

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Nechepurenko, M., Torgan, G. On the existence of a generalized solution of a nonlinear evolution system of equations in a domain unbounded in time. J Math Sci 173, 378–396 (2011). https://doi.org/10.1007/s10958-011-0256-3

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  • DOI: https://doi.org/10.1007/s10958-011-0256-3

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