Access the full text.
Sign up today, get DeepDyve free for 14 days.
M. Conti, E. Marchini, V. Pata (2012)
APPROXIMATING INFINITE DELAY WITH FINITE DELAYCommunications in Contemporary Mathematics, 14
M. Conti, E.M. Marchini, V. Pata (2010)
Semilinear wave equations of viscoelasticity in the minimal state framework, Discrete ContinDyn. Syst., 27
M. Conti, S. Gatti, M. Grasselli, V. Pata (2010)
Two-dimensional reaction-diffusion equations with memoryQuarterly of Applied Mathematics, 68
I. Cioranescu, C. Lizama (2003)
On the inversion of the Laplace transform for resolvent families in UMD spacesArch. Math. (Basel), 81
(1983)
Semigroups of linear operators and applications to partial differential equations
S. Gatti, A. Miranville, V. Pata, S. Zelik (2008)
Attractors for Semi-Linear Equations of Viscoelasticity with Very Low DissipationRocky Mountain Journal of Mathematics, 38
Xunjing Li, J. Yong (1994)
Optimal Control Theory for Infinite Dimensional Systems
M. Budyko (2008)
The Effects of Changing the Solar Constant on the Climate of a General Circulation Model
G. Prato, M. Iannelli (1985)
Existence and Regularity for a Class of Integrodifferential Equations of Parabolic TypeJournal of Mathematical Analysis and Applications, 112
(1994)
Approximate controllability for some simple climate models, Environment, Economic and their Mathematical Models
A. Cellina, A. Ferriero, E. Marchini (2003)
Reparametrizations and approximate values of integrals of the calculus of variationsJournal of Differential Equations, 193
J.-P. Aubin, H. Frankowska (1990)
Set-valued analysis
A. Bensoussan, M. Delfour, G. Prato, S. Mitter (1992)
Representation and Control of Infinite Dimensional Systems
P. Davis (1978)
On the Linear Theory of Heat Conduction for Materials with MemorySiam Journal on Mathematical Analysis, 9
L. Boltzmann (1878)
Zur Theorie der elastischen NachwirkungWied. Ann., 5
(1994)
Controllability and obstruction for some non linear parabolic problems in Climatology, Modelado de Sistemas en Oceanografa
C. Dafermos (1970)
Asymptotic stability in viscoelasticityArchive for Rational Mechanics and Analysis, 37
David Russel (1995)
Representation and Control of Infinite Dimensional Systems, Vols. 1 and 2 (A. Bensonssan, G. Da Prato, M. Delfour, and S. Mitter)SIAM Rev., 37
V. Barbu (1993)
Analysis and control of nonlinear infinite dimensional systems
M.I. Budyko (1969)
The effect of solar radiation variations on the climate of the earthTellus, 21
G. Prato, A. Lunardi (1988)
Solvability on the real line of a class of linear volterra integrodifferential equations of parabolic typeAnnali di Matematica Pura ed Applicata, 150
L. Boltzmann (1874)
Zur Theorie der elastischen NachwirkungWien. Ber., 70
V. Barbu, M. Iannelli (1999)
Optimal Control of Population DynamicsJournal of Optimization Theory and Applications, 102
(2013)
Can we survive technology
Nikolaos Papageorgiou (1991)
Nonlinear Volterra integrodifferential evolution inclusions and optimal controlKodai Mathematical Journal, 14
G. Carlier, R. Tahraoui (2008)
On some optimal control problems governed by a state equation with memoryESAIM: Control, Optimisation and Calculus of Variations, 14
H. Fattorini (1999)
Infinite Dimensional Optimization and Control Theory: References
M. Conti, E. Marchini (2011)
Wave equations with memory: the minimal state approachJournal of Mathematical Analysis and Applications, 384
(1969)
A climate model based on the energy balance of the earth-atmosphere system
J. Nunziato (1971)
On heat conduction in materials with memoryQuarterly of Applied Mathematics, 29
P. Cannarsa, D. Sforza (2003)
Global solutions of abstract semilinear parabolic equations with memory termsNonlinear Differential Equations and Applications NoDEA, 10
H. Frankowska (1990)
A priori estimates for operational differential inclusionsJournal of Differential Equations, 84
V. Volterra (1912)
Sur les équations intégro-différentielles et leurs applicationsActa Mathematica, 35
(1965)
Real and abstract
B. Coleman, M. Gurtin (1967)
Equipresence and constitutive equations for rigid heat conductorsZeitschrift für angewandte Mathematik und Physik ZAMP, 18
(1985)
Laplace transform methods in integrodifferential equations
(1878)
Zur Theorie der elastischen Nachwirkung , Wied
H. Grabmüller (1976–77)
On linear theory of heat conduction in materials with memoryProc. Roy. Soc. Edinburgh Sect. A, 76
P. Cannarsa, H. Frankowska (1992)
Value function and optimality conditions for semilinear control problemsApplied Mathematics and Optimization, 26
E. Hewitt, K. Stromberg (1965)
Real and abstract analysis
H.O. Fattorini (1999)
Infinite-dimensional optimization and control theory
M. Lavrentieff (1927)
Sur quelques problèmes du calcul des variationsAnnali di Matematica Pura ed Applicata, 4
I. Lasiecka, R. Triggiani (2000)
Control Theory for Partial Differential Equations: Continuous and Approximation Theories
(1993)
Evolutionary integral equations and applications, Birkhäuser Verlag, Basel
I. Ciorǎnescu, C. Lizama (2003)
On the inversion of the Laplace transform for resolvent families in UMD spacesArchiv der Mathematik, 81
R. Miller (1978)
An integrodifferential equation for rigid heat conductors with memoryJournal of Mathematical Analysis and Applications, 66
V. Chepyzhov, V. Pata (2006)
Some remarks on stability of semigroups arising from linear viscoelasticityAsymptot. Anal., 46
M. Conti, E. Marchini, V. Pata (2010)
Semilinear wave equations of viscoelasticity in the minimal state frameworkDiscrete and Continuous Dynamical Systems, 27
M. Conti, V. Pata, M. Squassina (2006)
Singular limit of differential systems with memoryIndiana University Mathematics Journal, 55
Singiresu Rao, R. Desai (1980)
Optimization Theory and ApplicationsIEEE Transactions on Systems, Man, and Cybernetics, 10
J. Prüss (1993)
Evolutionary integral equations and applications
M. Haase (2008)
THE COMPLEX INVERSION FORMULA REVISITEDJournal of the Australian Mathematical Society, 84
S. Londen, J. Nohel (1982)
A Nonlinear Volterra Integrodifferential Equation Occurring in Heat Flow.
M. Renardy, W. Hrusa, J. Nohel (1987)
Mathematical problems in viscoelasticity
V. Volterra (1913)
Leçons sur les fonctions de lignes
M. Fabrizio, A. Morro (1987)
Mathematical problems in linear viscoelasticity
D. Gao (2007)
NONCONVEX MINIMIZATION PROBLEMS
P. Cannarsa, D. Sforza (2003)
Global solutions of abstract semilinear parabolic equations with memory termsNoDEA Nonlinear Differential Equations Appl., 10
V. Pata (2006)
Exponential stability in linear viscoelasticityQuarterly of Applied Mathematics, 64
M. Chekroun, F. Plinio, N. Glatt-Holtz, V. Pata (2010)
Asymptotics of the Coleman-Gurtin modelarXiv: Analysis of PDEs
V. Pata (2010)
Exponential stability in linear viscoelasticity with almost flat memory kernelsCommunications on Pure and Applied Analysis, 9
B. Coleman, V. Mizel (1968)
On the general theory of fading memoryArchive for Rational Mechanics and Analysis, 29
B. Coleman, V. Mizel (1966)
Norms and semi-groups in the theory of fading memoryArchive for Rational Mechanics and Analysis, 23
Leçons sur les fonctions de lignes , Gauthier - Villars , Paris , 1913 . P . Cannarsa Dipartimento di Matematica , Università di Roma “ Tor Vergata ”
(1990)
Set-valued analysis, Birkhäuser
H. Frankowska, E. Marchini (2006)
Lipschitzianity of optimal trajectories for the Bolza optimal control problemCalculus of Variations and Partial Differential Equations, 27
In this paper, we investigate the existence and regularity of solutions for Bolza optimal control problems in infinite dimension governed by a class of semilinear evolution equations. Our results apply to systems exhibiting hereditary properties, as heat propagation in real conductors and isothermal viscoelasticity, described by equations with memory terms which account for the past history of the variables in play.
Journal of Evolution Equations – Springer Journals
Published: Mar 1, 2013
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.