This article is cited in 25 papers

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

M. Kirane^a, N.-e. Tatar<sup>b

a</sup> Université de La Rochelle
^b King Fahd University of Petroleum and Minerals

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.

Keywords: dynamical boundary conditions, fractional derivatives, nonexistence of global solutions, Poisson equations, test function method.

UDC: 517.957

Received: 17.10.2005
Revised: 20.02.2006

 English version: Siberian Mathematical Journal, 2007, 48:3, 477–488

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