Nonexistence of global solutions to an elliptic equation with a dynamical boundary condition

Mokhtar Kirane; Eric Nabana; Stanislav I. Pohozaev

doi:10.5269/bspm.v22i2.7475

Nonexistence of global solutions to an elliptic equation with a dynamical boundary condition

Mokhtar Kirane, Eric Nabana, Stanislav I. Pohozaev

Mathematics

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15 Scopus citations

Abstract

We consider the equation Δu = 0 posed in Q := (0;+1) × Ω;Ω := {x = (x'; xN)=x' ε R^N-1; xN > 0}; with the dynamical boundary condition B(t; x'; 0)u_tt + A(t; x'; 0)ut - uxN ≥ D(t; x'; 0)|u|^q on Σ := (0;∞) × R ^N-1 × {0} and give conditions on the coefficient functions A(t; x'; 0);B(t; x'; 0) and D(t; x'; 0) for the nonexistence of global solutions.

Original language	British English
Pages (from-to)	9-16
Number of pages	8
Journal	Boletim da Sociedade Paranaense de Matematica
Volume	22
Issue number	2
DOIs	https://doi.org/10.5269/bspm.v22i2.7475
State	Published - 2004

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abstract = "We consider the equation Δu = 0 posed in Q := (0;+1) × Ω;Ω := {x = (x'; xN)=x' ε RN-1; xN > 0}; with the dynamical boundary condition B(t; x'; 0)utt + A(t; x'; 0)ut - uxN ≥ D(t; x'; 0)|u|q on Σ := (0;∞) × R N-1 × {0} and give conditions on the coefficient functions A(t; x'; 0);B(t; x'; 0) and D(t; x'; 0) for the nonexistence of global solutions.",

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AU - Kirane, Mokhtar

AU - Nabana, Eric

AU - Pohozaev, Stanislav I.

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N2 - We consider the equation Δu = 0 posed in Q := (0;+1) × Ω;Ω := {x = (x'; xN)=x' ε RN-1; xN > 0}; with the dynamical boundary condition B(t; x'; 0)utt + A(t; x'; 0)ut - uxN ≥ D(t; x'; 0)|u|q on Σ := (0;∞) × R N-1 × {0} and give conditions on the coefficient functions A(t; x'; 0);B(t; x'; 0) and D(t; x'; 0) for the nonexistence of global solutions.

AB - We consider the equation Δu = 0 posed in Q := (0;+1) × Ω;Ω := {x = (x'; xN)=x' ε RN-1; xN > 0}; with the dynamical boundary condition B(t; x'; 0)utt + A(t; x'; 0)ut - uxN ≥ D(t; x'; 0)|u|q on Σ := (0;∞) × R N-1 × {0} and give conditions on the coefficient functions A(t; x'; 0);B(t; x'; 0) and D(t; x'; 0) for the nonexistence of global solutions.

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JF - Boletim da Sociedade Paranaense de Matematica

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ER -

Nonexistence of global solutions to an elliptic equation with a dynamical boundary condition

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