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Exponential stability for a class of linear hyperbolic equations with hereditary memory

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  • We establish a necessary and sufficient condition of exponential stability for the contraction semigroup generated by an abstract version of the linear differential equation $$∂_t u(t)-\int_0^\infty k(s)\Delta u(t-s)ds = 0 $$ modeling hereditary heat conduction of Gurtin-Pipkin type.
    Mathematics Subject Classification: 35B40, 45K05, 45M10, 47D03.


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