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On the Blow-Up of the Solution of a Problem for the Sobolev Equation with a Noncoercive Source

  • PARTIAL DIFFERENTIAL EQUATIONS
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Abstract

We consider an initial–boundary value problem for a nonlinear Sobolev-type second-order differential equation with a noncoercive source describing the behavior of charges in a semiconductor plasma in an external field. The local solvability of this problem is proved, and upper bounds are obtained for the solution blow-up time.

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REFERENCES

  1. Artem’eva, M.V. and Korpusov, M.O., Blow-up of solutions and local solvability of an abstract Cauchy problem of second order with a noncoercive source, Comput. Math. Math. Phys., 2023, vol. 63, no. 4, pp. 542–552.

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  2. Gajewski, H., Gröger, K., and Zacharias, K., Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen, Berlin: Akademie-Verlag, 1974. Translated under the title: Nelineinye operatornye uravneniya i operatornye differentsial’nye uravneniya, Moscow: Mir, 1978.

  3. Al’shin, A.B., Korpusov, M.O., and Sveshnikov, A.G., Blow-up in nonlinear Sobolev type equations, De Gruyter Ser. Nonlinear Anal. Appl., 2011, vol. 15, p. 648.

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  4. Korpusov, M.O., Blow-up and global solubility in the classical sense of the Cauchy problem for a formally hyperbolic equation with a non-coercive source, Izv. Math., 2020, vol. 84, no. 5, pp. 930–959.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, 119991, Russia

    M. V. Artemeva & M. O. Korpusov

  2. National Research Nuclear University MEPhI, Moscow, 115409, Russia

    M. V. Artemeva

Authors
  1. M. V. Artemeva
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  2. M. O. Korpusov
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Corresponding authors

Correspondence to M. V. Artemeva or M. O. Korpusov.

Additional information

Translated by V. Potapchouck

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Artemeva, M.V., Korpusov, M.O. On the Blow-Up of the Solution of a Problem for the Sobolev Equation with a Noncoercive Source. Diff Equat 59, 893–903 (2023). https://doi.org/10.1134/S0012266123070030

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  • DOI: https://doi.org/10.1134/S0012266123070030

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