Unified stability analysis for a Volterra integro-differential equation under creation time perspective

Many real-world applications are modeled by Volterra integral–differential equations of the form u tt - Δ u + ∫ α t g ( t - s ) Δ u ( s ) d s = 0 in Ω × ( 0 , ∞ ) , where Ω is a bounded domain of R N and g is a memory kernel. Our main concern is with the concept of so-called creation time , the time...

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Bibliographic Details
Published in:Zeitschrift für angewandte Mathematik und Physik 2022, Vol.73 (3), Article 118
Main Authors: Gomes Tavares, Eduardo H., Jorge Silva, Marcio A., Ma, To Fu
Format: Article
Language:English
Subjects:
Differential equations
Engineering
Limit analysis
Mathematical Methods in Physics
Stability analysis
Theoretical and Applied Mechanics
Volterra integral equations
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Summary:Many real-world applications are modeled by Volterra integral–differential equations of the form u tt - Δ u + ∫ α t g ( t - s ) Δ u ( s ) d s = 0 in Ω × ( 0 , ∞ ) , where Ω is a bounded domain of R N and g is a memory kernel. Our main concern is with the concept of so-called creation time , the time α where past history begins. Separately, the cases α = - ∞ (history) and α = 0 (null history) were extensively studied in the literature. However, as far as we know, there is no unified approach with respect to the intermediate case - ∞ < α < 0 . Therefore we provide new stability results featuring ( i ) uniform and general stability when the creation time α varies over full range ( - ∞ , 0 ) and ( ii ) connection between the history and the null history cases by means of a rigorous backward ( α → - ∞ ) and forward ( α → 0 - ) limit analysis.
ISSN:0044-2275
1420-9039
DOI:10.1007/s00033-022-01756-2