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Absence of local and global solutions to an elliptic system with time-fractional dynamical boundary conditions

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Abstract

This paper presents extensions of some nonexistence results for elliptic systems with dynamical boundary conditions involving the time-derivatives of integer orders to the case of noninteger order. In particular, we consider a system of Poisson’s equations with time-fractional derivatives of order less than one in the boundary conditions and specify the thresholds of the nonlinearities which lead to the absence of global solutions. The fractional derivatives here are meant in the Riemann-Liouville sense (or in the Caputo sense). We also present necessary conditions for the existence of local solutions.

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Authors and Affiliations

  1. Université de La Rochelle, La Rochelle, France

    Mokhtar Kirane

  2. King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia

    Nasser-Eddine Tatar

Authors
  1. Mokhtar Kirane
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  2. Nasser-Eddine Tatar
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Original Russian Text Copyright © 2007 Kirane M. and Tatar N.

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 48, No. 3, pp. 593–605, May–June, 2007.

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Kirane, M., Tatar, NE. Absence of local and global solutions to an elliptic system with time-fractional dynamical boundary conditions. Sib Math J 48, 477–488 (2007). https://doi.org/10.1007/s11202-007-0050-0

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  • DOI: https://doi.org/10.1007/s11202-007-0050-0

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