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Polynomial-in-time upper bounds for the orbital instability of subcritical generalized Korteweg-de Vries equations
Continuous dependence in hyperbolic problems with Wentzell boundary conditions
1. | Department of Mathematics, University of Bari, Via E. Orabona 4, I--70125 Bari, Italy, Italy |
2. | Dipartimento di Matematica, Università degli Studi di Bologna, Piazza di Porta S. Donato, 5, 40126 Bologna |
3. | The University of Memphis, Department of Mathematical Sciences, Memphis, TN 38152, United States |
4. | Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, United States |
References:
[1] |
S. Agmon, A. Douglis and L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I,, Comm. Pure Appl. Math., 12 (1959), 623.
doi: 10.1002/cpa.3160120405. |
[2] |
S. Agmon and L. Nirenberg, Properties of solutions of ordinary differential equations in Banach space,, Comm. Pure Appl. Math., 16 (1963), 121.
doi: 10.1002/cpa.3160160204. |
[3] |
G. M. Coclite, A Favini, C. G. Gal, G. R. Goldstein, J. A. Goldstein, E. Obrecht and S. Romanelli, The role of Wentzell boundary conditions in linear and nonlinear analysis,, In, (2009), 279.
|
[4] |
G. M. Coclite, A. Favini, G. R. Goldstein, J. A. Goldstein and S. Romanelli, Continuous dependence on the boundary conditions for the Wentzell Laplacian,, Semigroup Forum, 77 (2008), 101.
doi: 10.1007/s00233-008-9068-2. |
[5] |
K.-J. Engel and R. Nagel, "One-Parameter Semigroups for Linear Evolution Equations,", Graduate Texts in Mathematics, (2000).
|
[6] |
A. Favini, G. R. Goldstein, J. A. Goldstein and S. Romanelli, The heat equation with generalized Wentzell boundary conditions,, J. Evol. Equ., 2 (2002), 1.
doi: 10.1007/s00028-002-8077-y. |
[7] |
A. Favini, G. R. Goldstein, J. A. Goldstein, E. Obrecht and S. Romanelli, Elliptic operators with general Wentzell boundary conditions, analytic semigroups and the angle concavity theorem,, Math. Nachr., 283 (2010), 504.
doi: 10.1002/mana.200910086. |
[8] |
J. A. Goldstein, "Semigroups of Linear Operators and Applications,", Oxford University Press, (1985).
doi: 10.1016/0022-1236(69)90020-2. |
[9] |
J. A. Goldstein, Time dependent hyperbolic equations,, J. Functional Analysis, 4 (1969), 31.
|
[10] |
J. A. Goldstein and G. Reyes, Asymptotic equipartition of operator-weighted energies in damped wave equations,, {Asymptotic Analysis}, (). Google Scholar |
[11] |
T. Kato, "Perturbation Theory for Linear Operators,", Die Grundlehren der mathematischen Wissenschaften, (1966).
|
[12] |
P. D. Lax, "Functional Analysis,", Pure and Applied Mathematics (New York). Wiley-Interscience [John Wiley & Sons], (2002).
|
[13] |
J.-L. Lions and E. Magenes, "Non-Homogeneous Boundary Value Problems and Applications. Vol. I,", Die Grundlehren der mathematischen Wissenschaften, (1972).
|
[14] |
H. Triebel, "Theory of Function Spaces,", Monographs in Mathematics, (1983).
doi: 10.1007/978-3-0346-0416-1. |
show all references
References:
[1] |
S. Agmon, A. Douglis and L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I,, Comm. Pure Appl. Math., 12 (1959), 623.
doi: 10.1002/cpa.3160120405. |
[2] |
S. Agmon and L. Nirenberg, Properties of solutions of ordinary differential equations in Banach space,, Comm. Pure Appl. Math., 16 (1963), 121.
doi: 10.1002/cpa.3160160204. |
[3] |
G. M. Coclite, A Favini, C. G. Gal, G. R. Goldstein, J. A. Goldstein, E. Obrecht and S. Romanelli, The role of Wentzell boundary conditions in linear and nonlinear analysis,, In, (2009), 279.
|
[4] |
G. M. Coclite, A. Favini, G. R. Goldstein, J. A. Goldstein and S. Romanelli, Continuous dependence on the boundary conditions for the Wentzell Laplacian,, Semigroup Forum, 77 (2008), 101.
doi: 10.1007/s00233-008-9068-2. |
[5] |
K.-J. Engel and R. Nagel, "One-Parameter Semigroups for Linear Evolution Equations,", Graduate Texts in Mathematics, (2000).
|
[6] |
A. Favini, G. R. Goldstein, J. A. Goldstein and S. Romanelli, The heat equation with generalized Wentzell boundary conditions,, J. Evol. Equ., 2 (2002), 1.
doi: 10.1007/s00028-002-8077-y. |
[7] |
A. Favini, G. R. Goldstein, J. A. Goldstein, E. Obrecht and S. Romanelli, Elliptic operators with general Wentzell boundary conditions, analytic semigroups and the angle concavity theorem,, Math. Nachr., 283 (2010), 504.
doi: 10.1002/mana.200910086. |
[8] |
J. A. Goldstein, "Semigroups of Linear Operators and Applications,", Oxford University Press, (1985).
doi: 10.1016/0022-1236(69)90020-2. |
[9] |
J. A. Goldstein, Time dependent hyperbolic equations,, J. Functional Analysis, 4 (1969), 31.
|
[10] |
J. A. Goldstein and G. Reyes, Asymptotic equipartition of operator-weighted energies in damped wave equations,, {Asymptotic Analysis}, (). Google Scholar |
[11] |
T. Kato, "Perturbation Theory for Linear Operators,", Die Grundlehren der mathematischen Wissenschaften, (1966).
|
[12] |
P. D. Lax, "Functional Analysis,", Pure and Applied Mathematics (New York). Wiley-Interscience [John Wiley & Sons], (2002).
|
[13] |
J.-L. Lions and E. Magenes, "Non-Homogeneous Boundary Value Problems and Applications. Vol. I,", Die Grundlehren der mathematischen Wissenschaften, (1972).
|
[14] |
H. Triebel, "Theory of Function Spaces,", Monographs in Mathematics, (1983).
doi: 10.1007/978-3-0346-0416-1. |
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