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1. | Department of Mathematics, University of Missouri, Columbia, MO 65211, United States |
References:
[1] |
H. Amann, Operator-valued Fourier multipliers, vector-valued Besov spaces, and applications, Math. Nachr., 186 (1997), 5-56.
doi: 10.1002/mana.3211860102. |
[2] |
W. Arendt, C. J. K. Batty, M. Hieber and F. Neubrander, "Vector-Valued Laplace transforms and Cauchy Problems," Springer-Verlag, New York, 2011. |
[3] |
C. Chicone and Y. Latushkin, "Evolution Semigroups in Dynamical Systems and Differential Equations," Math. Surv. Monogr., 70, AMS, Providence, 1999. |
[4] |
K. Engel and R. Nagel, "One-Parameter Semigroups for Linear Evolution Equations," Springer-Verlag, New York, 2000. |
[5] |
A. Ghazaryan, A. Hoffman, K. Promislov and S. Schecter, Private Communications. |
[6] |
A. Ghazaryan, Y. Latushkin and S. Schecter, Stability of traveling waves for a class of reaction-diffusion systems that arise in chemical reaction models, SIAM J. Mathematical Analysis, 42 (2010), 2434-2472.
doi: 10.1137/100786204. |
[7] |
A. Ghazaryan, Y. Latushkin and S. Schecter, Stability of traveling waves for degenerate systems of reaction diffusion equations, Indiana University Math. J., 60 (2011), 443-471.
doi: 10.1512/iumj.2011.60.4069. |
[8] |
A. Ghazaryan, Y. Latushkin, S. Schecter and A. de Souza, Stability of gasless combustion fronts in one-dimensional solids, Archive Rational Mech. Anal., 198 (2010), 981-1030.
doi: 10.1007/s00205-010-0358-y. |
[9] |
A. Ghazaryan, Y. Latushkin, S. Schecter and V. Yurov, Spectral mapping results for degenerate systems, (In preparation). |
[10] |
J. Goldstein, "Semigroups of Linear Operators and Applications," Oxford Univ. Press, New York, 1985. |
[11] |
B. Helffer and J. Sjöstrand, From resolvent bounds to semigroup bounds, preprint (2010) arXiv:1001.4171v1. |
[12] |
M. Hieber, Operator valued Fourier multipliers, Progress in Nonlinear Differential Equations and Their Applications, 35 (1999), 363-380. |
[13] |
M. Hieber, A characterization of the growth bound of a semigroup via Fourier multipliers, in "Evolution Equations and Their Applications in Physical and Life Sciences (Bad Herrenalb, 1998), 121-124, Lecture Notes in Pure and Appl. Math., 215, Dekker, New York, (2001). |
[14] |
Y. Latushkin and F. Räbiger, Operator valued Fourier multipliers and stability of strongly continuous semigroups, Integral Eqns. Oper. Theory, 51 (2005), 375-394.
doi: 10.1007/s00020-004-1349-x. |
[15] |
Y. Latushkin and R. Shvydkoy, "Hyperbolicity of Semigroups and Fourier Multipliers," Systems, Approximation, Singular Integral Operators, and Related Topics (Bordeaux, 2000), 341-363, Oper. Theory Adv. Appl., 129, Birkhäuser, Basel, 2001. |
[16] |
J. M. A. M. van Neerven, "The Asymptotic Behavior of Semigroups of Linear Operators," Oper. Theory Adv. Appl., 88, Birkhäuser-Verlag, 1996.
doi: 10.1007/978-3-0348-9206-3. |
[17] |
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. |
show all references
References:
[1] |
H. Amann, Operator-valued Fourier multipliers, vector-valued Besov spaces, and applications, Math. Nachr., 186 (1997), 5-56.
doi: 10.1002/mana.3211860102. |
[2] |
W. Arendt, C. J. K. Batty, M. Hieber and F. Neubrander, "Vector-Valued Laplace transforms and Cauchy Problems," Springer-Verlag, New York, 2011. |
[3] |
C. Chicone and Y. Latushkin, "Evolution Semigroups in Dynamical Systems and Differential Equations," Math. Surv. Monogr., 70, AMS, Providence, 1999. |
[4] |
K. Engel and R. Nagel, "One-Parameter Semigroups for Linear Evolution Equations," Springer-Verlag, New York, 2000. |
[5] |
A. Ghazaryan, A. Hoffman, K. Promislov and S. Schecter, Private Communications. |
[6] |
A. Ghazaryan, Y. Latushkin and S. Schecter, Stability of traveling waves for a class of reaction-diffusion systems that arise in chemical reaction models, SIAM J. Mathematical Analysis, 42 (2010), 2434-2472.
doi: 10.1137/100786204. |
[7] |
A. Ghazaryan, Y. Latushkin and S. Schecter, Stability of traveling waves for degenerate systems of reaction diffusion equations, Indiana University Math. J., 60 (2011), 443-471.
doi: 10.1512/iumj.2011.60.4069. |
[8] |
A. Ghazaryan, Y. Latushkin, S. Schecter and A. de Souza, Stability of gasless combustion fronts in one-dimensional solids, Archive Rational Mech. Anal., 198 (2010), 981-1030.
doi: 10.1007/s00205-010-0358-y. |
[9] |
A. Ghazaryan, Y. Latushkin, S. Schecter and V. Yurov, Spectral mapping results for degenerate systems, (In preparation). |
[10] |
J. Goldstein, "Semigroups of Linear Operators and Applications," Oxford Univ. Press, New York, 1985. |
[11] |
B. Helffer and J. Sjöstrand, From resolvent bounds to semigroup bounds, preprint (2010) arXiv:1001.4171v1. |
[12] |
M. Hieber, Operator valued Fourier multipliers, Progress in Nonlinear Differential Equations and Their Applications, 35 (1999), 363-380. |
[13] |
M. Hieber, A characterization of the growth bound of a semigroup via Fourier multipliers, in "Evolution Equations and Their Applications in Physical and Life Sciences (Bad Herrenalb, 1998), 121-124, Lecture Notes in Pure and Appl. Math., 215, Dekker, New York, (2001). |
[14] |
Y. Latushkin and F. Räbiger, Operator valued Fourier multipliers and stability of strongly continuous semigroups, Integral Eqns. Oper. Theory, 51 (2005), 375-394.
doi: 10.1007/s00020-004-1349-x. |
[15] |
Y. Latushkin and R. Shvydkoy, "Hyperbolicity of Semigroups and Fourier Multipliers," Systems, Approximation, Singular Integral Operators, and Related Topics (Bordeaux, 2000), 341-363, Oper. Theory Adv. Appl., 129, Birkhäuser, Basel, 2001. |
[16] |
J. M. A. M. van Neerven, "The Asymptotic Behavior of Semigroups of Linear Operators," Oper. Theory Adv. Appl., 88, Birkhäuser-Verlag, 1996.
doi: 10.1007/978-3-0348-9206-3. |
[17] |
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. |
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