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Waves and diffusion on metric graphs with general vertex conditions
Two questions arising in the theory of attractors
Politecnico di Milano - Dipartimento di Matematica, Via Bonardi 9, 20133 Milano, Italy |
In this note, we dwell on the notions of global and exponential attractors for strongly continuous semigroups acting on a complete metric space. Two natural questions arising in the theory are addressed.
References:
[1] |
A. V. Babin and M. I. Vishik, Attractors of Evolution Equations, North-HollandAmsterdam, 1992. |
[2] |
V. V. Chepyzhov and M. I. Vishik, Attractors for Equations of Mathematical Physics, Amer. Math. Soc. Providence, 2002. |
[3] |
A. Eden, C. Foias, B. Nicolaenko and R. Temam, Exponential Attractors for Dissipative Evolution Equations, MassonParis, 1994. |
[4] |
M. Efendiev, A. Miranville and S. Zelik,
Exponential attractors for a nonlinear reaction-diffusion system in ${\mathbb R}^3$, C.R. Acad. Sci. Paris Sér. I Math., 330 (2000), 713-718.
doi: 10.1016/S0764-4442(00)00259-7. |
[5] |
J. K. Hale, Asymptotic Behavior of Dissipative Systems, Amer. Math. Soc. Providence, 1988. |
[6] |
A. Haraux, Systèmes Dynamiques Dissipatifs Et Applications, MassonParis, 1991. |
[7] |
A. Miranville and S. Zelik, Attractors for dissipative partial differential equations in bounded and unbounded domains, Handbook of Differential Equations: Evolutionary Equations, Handb. Differ. Equ., Elsevier/North-Holland, Amsterdam, 4 (2008), 103–200.
doi: 10.1016/S1874-5717(08)00003-0. |
[8] |
A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983.
doi: 10.1007/978-1-4612-5561-1. |
[9] |
R. Temam, Infinite-dimensional Dynamical Systems in Mechanics and Physics, Springer, New York, 1997.
doi: 10.1007/978-1-4612-0645-3. |
show all references
References:
[1] |
A. V. Babin and M. I. Vishik, Attractors of Evolution Equations, North-HollandAmsterdam, 1992. |
[2] |
V. V. Chepyzhov and M. I. Vishik, Attractors for Equations of Mathematical Physics, Amer. Math. Soc. Providence, 2002. |
[3] |
A. Eden, C. Foias, B. Nicolaenko and R. Temam, Exponential Attractors for Dissipative Evolution Equations, MassonParis, 1994. |
[4] |
M. Efendiev, A. Miranville and S. Zelik,
Exponential attractors for a nonlinear reaction-diffusion system in ${\mathbb R}^3$, C.R. Acad. Sci. Paris Sér. I Math., 330 (2000), 713-718.
doi: 10.1016/S0764-4442(00)00259-7. |
[5] |
J. K. Hale, Asymptotic Behavior of Dissipative Systems, Amer. Math. Soc. Providence, 1988. |
[6] |
A. Haraux, Systèmes Dynamiques Dissipatifs Et Applications, MassonParis, 1991. |
[7] |
A. Miranville and S. Zelik, Attractors for dissipative partial differential equations in bounded and unbounded domains, Handbook of Differential Equations: Evolutionary Equations, Handb. Differ. Equ., Elsevier/North-Holland, Amsterdam, 4 (2008), 103–200.
doi: 10.1016/S1874-5717(08)00003-0. |
[8] |
A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983.
doi: 10.1007/978-1-4612-5561-1. |
[9] |
R. Temam, Infinite-dimensional Dynamical Systems in Mechanics and Physics, Springer, New York, 1997.
doi: 10.1007/978-1-4612-0645-3. |


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