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2007 A Note on the Parabolic Differential and Difference Equations
Allaberen Ashyralyev, Yasar Sozen, Pavel E. Sobolevskii
Abstr. Appl. Anal. 2007: 1-16 (2007). DOI: 10.1155/2007/61659

Abstract

The differential equation u ' ( t ) + A u ( t ) = f ( t ) ( < t < ) in a general Banach space E with the strongly positive operator A is ill-posed in the Banach space C ( E ) = C ( , E ) with norm ϕ C ( E ) = sup < t < ϕ ( t ) E . In the present paper, the well-posedness of this equation in the Hölder space C α ( E ) = C α ( , E ) with norm ϕ C α ( E ) = sup < t < ϕ ( t ) E + sup < t < t + s < (‖ ϕ ( t + s ) ϕ ( t ) E / s α ), 0 < α < 1 , is established. The almost coercivity inequality for solutions of the Rothe difference scheme in C ( τ , E ) spaces is proved. The well-posedness of this difference scheme in C α ( τ , E ) spaces is obtained.

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Allaberen Ashyralyev. Yasar Sozen. Pavel E. Sobolevskii. "A Note on the Parabolic Differential and Difference Equations." Abstr. Appl. Anal. 2007 1 - 16, 2007. https://doi.org/10.1155/2007/61659

Information

Published: 2007
First available in Project Euclid: 5 July 2007

zbMATH: 1153.35353
MathSciNet: MR2302192
Digital Object Identifier: 10.1155/2007/61659

Rights: Copyright © 2007 Hindawi

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