A duality approach for solving identification problems related to integrodifferential Maxwell's equations
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A. Lorenzi, V. Priymenko (1994)
Rendiconti del Seminario Matematico della Università di Padova
P. Ch. Tsamatos, S. K. Ntouyas, B. C. Dhage (2002)
Δελτίο της Ελληνικής Μαθηματικής Εταιρίας
Lorenzi, A. (1999)
Zeitschrift für Analysis und ihre Anwendungen
Zhan-Dong Mei, Ji-Gen Peng, Jun-Xiong Jia (2014)
Studia Mathematica
A new characteristic property of the Mittag-Leffler function with 1 < α < 2 is deduced. Motivated by this property, a new notion, named α-order cosine function, is developed. It is proved that an α-order cosine function is associated with a solution operator of an α-order abstract Cauchy problem. Consequently, an α-order abstract Cauchy problem is well-posed if and only if its coefficient operator generates a unique α-order cosine function.
Benchohra, Mouffak (2000)
Mathematica Pannonica
Liu, James H. (1993)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Piermarco Cannarsa, Daniela Sforza (2008)
Applicationes Mathematicae
We study second order nonlinear integro-differential equations in Hilbert spaces with weakly singular convolution kernels obtaining energy estimates for the solutions, uniform in t. Then we show that the solutions decay exponentially at ∞ in the energy norm. Finally, we apply these results to a problem in viscoelasticity.
Maurizio Grasselli, Alfredo Lorenzi (1991)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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.
Choulli, M. (1991)
Journal of Applied Mathematics and Stochastic Analysis
Chiş, Adela (2005)
Acta Universitatis Apulensis. Mathematics - Informatics
Emmanuele, Giovanni (1994)
Portugaliae Mathematica
Jaroslav Milota, Hana Petzeltová (1985)
Časopis pro pěstování matematiky
Stanisław Szufla (1984)
Commentationes Mathematicae Universitatis Carolinae
S. Mazouzi, Nasser-eddine Tatar (2003)
Archivum Mathematicum
We prove exponential decay for the solution of an abstract integrodifferential equation. This equation involves coefficients of polynomial type, weakly singular kernels as well as different powers of the unknown in some norms.
Marián Slodička (1990)
Aplikace matematiky
One parabolic integrodifferential problem in the abstract real Hilbert spaces is studied in this paper. The semidiscrete and full discrete approximate solution is defined and the error estimate of Rothe's function in some function spaces is established.
Couchouron, Jean-Francois, Precup, Radu (2004)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Stanisław Szufla (1984)
Commentationes Mathematicae Universitatis Carolinae
Stanislaw Szufla (1988)
Publications de l'Institut Mathématique
Bica, Alexandru, Căuş, Vasile Aurel, Mureşan, Sorin (2006)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
Hirokazu Oka, Naoki Tanaka (2000)
Studia Mathematica
This paper is devoted to the approximation of abstract linear integrodifferential equations by finite difference equations. The result obtained here is applied to the problem of convergence of the backward Euler type discrete scheme.
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