Geodesic
Abstract nonlinear Volterra integrodifferential equations with nonsmooth kernels
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 2 (1991) no. 1, pp. 43-53.

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A Cauchy problem for an abstract nonlinear Volterra integrodifferential equation is considered. Existence and uniqueness results are shown for any given time interval under weak time regularity assumptions on the kernel. Some applications to the heat flow with memory are presented.
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. 
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     title = {Abstract nonlinear {Volterra} integrodifferential equations with nonsmooth kernels},
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Grasselli, Maurizio; Lorenzi, Alfredo. Abstract nonlinear Volterra integrodifferential equations with nonsmooth kernels. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 2 (1991) no. 1, pp. 43-53. http://geodesic.mathdoc.fr/item/RLIN_1991_9_2_1_a5/

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

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

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

[4] G. Chen - R. Grimmer, Semigroups and integral equations. J. Int. Equations, 2, 1980, 133-154. | MR | Zbl

[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 | Zbl

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

[7] G. Gripenberg, Volterra integro-differential equations with accretive nonlinearity. J. Diff. Equations, 60, 1985, 57-79. | DOI | MR | Zbl

[8] M. L. Heard, An abstract parabolic Volterra integrodifferential equation. SIAM J. Math. Anal., 13, 1982, 81-105. | DOI | MR | Zbl

[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. | DOI | MR | Zbl

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

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

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

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

[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 | Zbl

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

[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 | Zbl

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