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Large time behavior of solution for the full compressible navier-stokes-maxwell system
Krasnosel'skii type formula and translation along trajectories method on the scale of fractional spaces
1. | Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Toruń, Poland |
References:
[1] |
A. Ćwiszewski, Topological degree methods for perturbations of operators generating compact $C_0$ semigroups,, \emph{Journal of Differential Equations}, 220 (2006), 434.
doi: 10.1016/j.jde.2005.04.007. |
[2] |
A. Ćwiszewski, Degree theory for perturbations of m-accretive operators generating compact semigroups with constraints,, \emph{Journal of Evolution Equations}, 7 (2007), 1.
doi: 10.1007/s00028-006-0225-3. |
[3] |
A. Ćwiszewski, Positive periodic solutions of parabolic evolution problems: A translation along trajectories approach,, \emph{Central European Journal of Mathematics}, 9 (2011), 244.
doi: 10.2478/s11533-011-0010-6. |
[4] |
A. Ćwiszewski, Forced oscillations in strongly damped beam equation,, \emph{Topol. Methods Nonlinear Anal.}, 37 (2011), 259.
|
[5] |
A. Ćwiszewski, Averaging principle and hyperbolic evolution equations,, \emph{Nonlinear Analysis: Theory, 75 (2012), 2362.
doi: 10.1016/j.na.2011.10.034. |
[6] |
A. Ćwiszewski and P. Kokocki, Krasnosel'skii type formula and translation along trajectories method for evolution equations,, \emph{Discrete Continuous Dynam. Systems - B}, 22 (2008), 605.
doi: 10.3934/dcds.2008.22.605. |
[7] |
A. Ćwiszewski and P. Kokocki, Periodic solutions of nonlinear hyperbolic evolution systems,, \emph{Journal of Evolution Equations}, 10 (2010), 677.
doi: 10.1007/s00028-010-0066-y. |
[8] |
J. W. Cholewa and T. Dłotko, Global Attractors in Abstract Parabolic Problems,, \emph{London Mathematical Society Lectures Note Series}, 278 (2000).
doi: 10.1017/CBO9780511526404. |
[9] |
K. J. Engel and R. Nagel, One-parameter semigroups for linear evolution equations,, \emph{Graduate Texts in Mathematics}, 194 (2000).
|
[10] |
M. Furi and M. P. Pera, Global bifurcation of fixed points and the Poincaré translation operator on manifolds,, \emph{Annali di Matematica pura ed applicata}, 173 (1997), 313.
doi: 10.1007/BF01783474. |
[11] |
M. Furi and M. P. Pera, A continuation principle for forced oscillations on differentiable manifolds,, \emph{Pacific Journal of Mathematics}, 121 (1986), 321.
|
[12] |
R. E. Gaines and J. Mawhin, Coincidence Degree and Nonlinear Differential Equations,, {Lecture Notes in Mathematics}, 586 (1977).
|
[13] |
D. Henry, Geometric Theory of Semilinear Parabolic Equations,, Springer-Verlag, (1981).
|
[14] |
E. Hille and R. Phillips, Functional Analysis and Semi-Groups,, American Mathematical Society, (1957).
|
[15] |
M. Kamenskii, O. Makarenkov and P. Nistri, A continuation principle for a class of periodically perturbed autonomous systems,, \emph{Mathematische Nachrichten}, 281 (2008), 42.
doi: 10.1002/mana.200610586. |
[16] |
P. Kokocki, Averaging principle and periodic solutions for nonlinear evolution equations at resonance,, \emph{Nonlinear Analysis: Theory, 85 (2013), 253.
doi: 10.1016/j.na.2013.02.030. |
[17] |
B. Laloux and J. Mawhin, Multiplicity, Leray-Schauder formula, and bifurcation,, \emph{Jourbal of Differential Equations}, 24 (1977), 309.
|
[18] |
J. Mawhin, Topological Degree Methods in Nonlinear Boundary Value Problems,, Amer. Math. Soc., (1979).
|
[19] |
J. Mawhin, Continuation theorems and periodic solutions of ordinary differential equations,, in \emph{Topological methods in differential equations and inclusions}, (1995).
|
[20] |
J. Mawhin, Continuation theorems for nonlinear operator equations: the legacy of Leray and Schauder,, \emph{Travaux mathmatiques}, (1999).
|
[21] |
J. Mawhin, Topological bifurcation theory: old and new,, \emph{Progress in variational methods}, (2011).
|
[22] |
A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations,, Springer-Verlag, (1983).
doi: 10.1007/978-1-4612-5561-1. |
[23] |
H. Triebel, Interpolation Theory, Function Spaces, Differential Operators,, VEB Deutscher Verlag der Wissenschaften, (1978).
|
show all references
References:
[1] |
A. Ćwiszewski, Topological degree methods for perturbations of operators generating compact $C_0$ semigroups,, \emph{Journal of Differential Equations}, 220 (2006), 434.
doi: 10.1016/j.jde.2005.04.007. |
[2] |
A. Ćwiszewski, Degree theory for perturbations of m-accretive operators generating compact semigroups with constraints,, \emph{Journal of Evolution Equations}, 7 (2007), 1.
doi: 10.1007/s00028-006-0225-3. |
[3] |
A. Ćwiszewski, Positive periodic solutions of parabolic evolution problems: A translation along trajectories approach,, \emph{Central European Journal of Mathematics}, 9 (2011), 244.
doi: 10.2478/s11533-011-0010-6. |
[4] |
A. Ćwiszewski, Forced oscillations in strongly damped beam equation,, \emph{Topol. Methods Nonlinear Anal.}, 37 (2011), 259.
|
[5] |
A. Ćwiszewski, Averaging principle and hyperbolic evolution equations,, \emph{Nonlinear Analysis: Theory, 75 (2012), 2362.
doi: 10.1016/j.na.2011.10.034. |
[6] |
A. Ćwiszewski and P. Kokocki, Krasnosel'skii type formula and translation along trajectories method for evolution equations,, \emph{Discrete Continuous Dynam. Systems - B}, 22 (2008), 605.
doi: 10.3934/dcds.2008.22.605. |
[7] |
A. Ćwiszewski and P. Kokocki, Periodic solutions of nonlinear hyperbolic evolution systems,, \emph{Journal of Evolution Equations}, 10 (2010), 677.
doi: 10.1007/s00028-010-0066-y. |
[8] |
J. W. Cholewa and T. Dłotko, Global Attractors in Abstract Parabolic Problems,, \emph{London Mathematical Society Lectures Note Series}, 278 (2000).
doi: 10.1017/CBO9780511526404. |
[9] |
K. J. Engel and R. Nagel, One-parameter semigroups for linear evolution equations,, \emph{Graduate Texts in Mathematics}, 194 (2000).
|
[10] |
M. Furi and M. P. Pera, Global bifurcation of fixed points and the Poincaré translation operator on manifolds,, \emph{Annali di Matematica pura ed applicata}, 173 (1997), 313.
doi: 10.1007/BF01783474. |
[11] |
M. Furi and M. P. Pera, A continuation principle for forced oscillations on differentiable manifolds,, \emph{Pacific Journal of Mathematics}, 121 (1986), 321.
|
[12] |
R. E. Gaines and J. Mawhin, Coincidence Degree and Nonlinear Differential Equations,, {Lecture Notes in Mathematics}, 586 (1977).
|
[13] |
D. Henry, Geometric Theory of Semilinear Parabolic Equations,, Springer-Verlag, (1981).
|
[14] |
E. Hille and R. Phillips, Functional Analysis and Semi-Groups,, American Mathematical Society, (1957).
|
[15] |
M. Kamenskii, O. Makarenkov and P. Nistri, A continuation principle for a class of periodically perturbed autonomous systems,, \emph{Mathematische Nachrichten}, 281 (2008), 42.
doi: 10.1002/mana.200610586. |
[16] |
P. Kokocki, Averaging principle and periodic solutions for nonlinear evolution equations at resonance,, \emph{Nonlinear Analysis: Theory, 85 (2013), 253.
doi: 10.1016/j.na.2013.02.030. |
[17] |
B. Laloux and J. Mawhin, Multiplicity, Leray-Schauder formula, and bifurcation,, \emph{Jourbal of Differential Equations}, 24 (1977), 309.
|
[18] |
J. Mawhin, Topological Degree Methods in Nonlinear Boundary Value Problems,, Amer. Math. Soc., (1979).
|
[19] |
J. Mawhin, Continuation theorems and periodic solutions of ordinary differential equations,, in \emph{Topological methods in differential equations and inclusions}, (1995).
|
[20] |
J. Mawhin, Continuation theorems for nonlinear operator equations: the legacy of Leray and Schauder,, \emph{Travaux mathmatiques}, (1999).
|
[21] |
J. Mawhin, Topological bifurcation theory: old and new,, \emph{Progress in variational methods}, (2011).
|
[22] |
A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations,, Springer-Verlag, (1983).
doi: 10.1007/978-1-4612-5561-1. |
[23] |
H. Triebel, Interpolation Theory, Function Spaces, Differential Operators,, VEB Deutscher Verlag der Wissenschaften, (1978).
|
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