Grasselli, Lorenzi: Abstract nonlinear Volterra integrodifferential equations with nonsmooth kernels

Grasselli, Maurizio and Lorenzi, Alfredo:
Abstract nonlinear Volterra integrodifferential equations with nonsmooth kernels (Equazioni integrodifferenziali astratte nonlineari di Volterra con nuclei non regolari)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni Serie 9 2 (1991), fasc. n.1, p. 43-53, (English)
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Si studia un problema di Cauchy per un'equazione integrodifferenziale astratta nonlineare di Volterra. Si provano risultati di esistenza e unicità supponendo il nucleo debolmente regolare rispetto al tempo. Si presentano alcune applicazioni dei risultati ottenuti a modelli di conduzione del calore con memoria.

Referenze Bibliografiche

[1] P. ACQUISTAPACE, Existence and maximal time regularity for linear parabolic integrodifferential equations. J. Int. Equations, 10, 1985, 5-43. | MR 831233 | Zbl 0584.45012

[2] S. AIZICOVICI, Time-dependent Volterra integrodifferential equations. Ibid., 45-60. | MR 831234 | Zbl 0587.45017

[3] J. R. CANNON - Y. LIN, Smooth solutions for an integro-differential equation of parabolic type. Diff. Int. Equations, 2, 1989, 111-121. | MR 960018 | Zbl 0719.45007

[4] G. CHEN - R. GRIMMER, Semigroups and integral equations. J. Int. Equations, 2, 1980, 133-154. | MR 572484 | Zbl 0449.45007

[5] M. G. CRANDALL - S.-O. LONDEN - J. A. NOHEL, An abstract nonlinear Volterra integrodifferential equation. J. Math. Anal. Appl, 64, 1978, 701-735. | MR 500052 | Zbl 0395.45023

[6] G. DI BLASIO, Nonautonomous integrodifferential equations in \( L^{p} \) spaces. J. Int. Equations, 10, 1985, 111-121. | MR 831238 | Zbl 0585.45006

[7] G. GRIPENBERG, Volterra integro-differential equations with accretive nonlinearity. J. Diff. Equations, 60, 1985, 57-79. | fulltext (doi) | MR 808257 | Zbl 0575.45013

[8] M. L. HEARD, An abstract parabolic Volterra integrodifferential equation. SIAM J. Math. Anal., 13, 1982, 81-105. | fulltext (doi) | MR 641542 | Zbl 0477.45008

[9] M. L. HEARD - S. M. RANKIN III, Weak solutions for a class of parabolic Volterra integrodifferential equations. J. Math. Anal. Appl., 139, 1989, 78-109. | fulltext (doi) | MR 991928 | Zbl 0681.45010

[10] J. L. LIONS, Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod, Paris 1969. | MR 259693 | Zbl 0189.40603

[11] J. L. LIONS - E. MAGENES, Non-Homogeneous Boundary Value Problems and Applications. Vol. I, Springer Verlag, Berlin 1972. | MR 350177 | Zbl 0223.35039

[12] S.-O. LONDEN - J. A. NOHEL, Nonlinear Volterra integrodifferential equation occuring in heat flow. J. Int. Equations, 6, 1984, 11-50. | MR 727934 | Zbl 0537.45011

[13] A. LUNARDI - E. SINESTRARI, Existence in the large and stability for nonlinear Volterra equations. Ibid., 213-239. | MR 831245 | Zbl 0587.45016

[14] J. A. NOHEL, Nonlinear Volterra Equations for Heat Flow in Materials with Memory. Integral and Functional Differential Equations, Lecture Notes in Pure and Applied Math., No. 67, Marcel Dekker, New York 1981, 3-82. | MR 617039 | Zbl 0465.45017

[15] J. W. NUNZIATO, On heat conduction in materials with memory. Quart. Appl. Math., 29, 1971, 187-204. | MR 295683 | Zbl 0227.73011

[16] E. SINESTRARI, An integrodifferential equation arising from the theory of nonlinear heat flow with memory. Nonlinear parabolic equations: qualitative properties of solutions, Pitman Res. Notes in Math., No. 149, Longman, Harlow 1987, 207-218. | MR 901111 | Zbl 0624.45016

[17] G. F. WEBB, An abstract semilinear Volterra integrodifferential equation. Proc. A.M.S., 69, 1978, 255-261. | MR 467214 | Zbl 0388.45012

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Referenze Bibliografiche