Fundamental solutions for wave equation in Robertson-Walker model of universeand $L^p-L^q$ -decay estimates

Karen Yagdjian; Anahit Galstian

doi:10.3934/dcdss.2009.2.483

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2009, Volume 2, Issue 3: 483-502. Doi: 10.3934/dcdss.2009.2.483

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Fundamental solutions for wave equation in Robertson-Walker model of universe and $L^p-L^q$ -decay estimates

Karen Yagdjian^1, and
Anahit Galstian^1,

1.
Department of Mathematics, University of Texas-Pan American, 1201 W. University Drive, Edinburg, TX 78541-2999

Received: September 2008

Revised: February 2009

Published: September 2009

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Abstract

We use constructed in [24] the fundamental solutions of the wave equation arising in the Robertson-Walker model of universe to derive the $L^p-L^q$-decay estimates for the solutions of the equation with and without a source term.

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Mathematics Subject Classification: Primary: 35L05; 35Q75; 35L15; Secondary: 35C15.

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Fundamental solutions for wave equation in Robertson-Walker model of universe and $L^p-L^q$ -decay estimates

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