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Direct and inverse problems in the theory of materials with memory. (English) Zbl 0757.73018

Summary: We prove some existence, uniqueness and stability results for a direct and an inverse problem related to the linear integrodifferential equations arising in the theory of materials with memory having a non- smooth memory function.

MSC:

74D99 Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials)
45J05 Integro-ordinary differential equations
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References:

[1] G. Da Prato , Abstract differential equations, maximal regularity and linearization , Proc. Symposia Pure Math. , Vol. 45 , part 1 ( 1986 ), pp. 359 - 370 . MR 843572 | Zbl 0594.34062 · Zbl 0594.34062
[2] G. Di Blasio , Linear parabolic equations in Lp-spaces , Ann. Mat. Pura Appl. , 138 ( 1984 ), pp. 55 - 104 . MR 779538 | Zbl 0568.35047 · Zbl 0568.35047
[3] G. Di Blasio , Nonautonomous integrodifferential equations in Lp-spaces , J. Int. Equations , 10 ( 1985 ), pp. 111 - 121 . MR 831238 | Zbl 0585.45006 · Zbl 0585.45006
[4] A. Lorenzi - E. Sinestrari , An inverse problem in the theory of materials with memory I , Nonlinear Anal. T.M.A. , 12 ( 1988 ), pp. 1317 - 1335 . MR 972401 | Zbl 0673.45010 · Zbl 0673.45010
[5] A. Lorenzi - E. Sinestrari , Stability results for a partial integrodifferential inverse problem , Pitman Research Notes in Math. , Vol. 190 ( 1989 ), pp. 271 - 294 . MR 1018886 | Zbl 0673.45011 · Zbl 0673.45011
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