
Previous Article
A variational approach to approximate controls for system with essential spectrum: Application to membranal arch
 EECT Home
 This Issue

Next Article
Orbitally stable standing waves for the asymptotically linear onedimensional NLS
Analyticity and regularity for a class of second order evolution equations
1.  Laboratoire JacquesLouis Lions, U.M.R C.N.R.S. 7598, Université Pierre et Marie Curie, Boite courrier 187, 75252 Paris Cedex 05, France 
2.  Department of Applied Physics, School of Science and Engineering, Waseda University, 341, Okubo, Shinjukuku, Tokyo, 1698555, Japan 
References:
[1] 
T. Cazenave and A. Haraux, "An Introduction to Semilinear Evolution Equations," Oxford Lecture Series in Mathematics and its Applications, 13, 1998. 
[2] 
G. Chen and D. L. Russell, A mathematical model for linear elastic systems with structural damping, Quart. Appl. Math., 39 (1981/82), 433454. 
[3] 
S. Chen and R. Triggiani, Proof of extension of two conjectures on structural damping for elastic systems: The case $\frac{1}{2} \le\alpha\le 1$, Pacific. J. Math., 136 (1989), 1555. 
[4] 
S. Chen and R. Triggiani, Gevrey class semigroups arising from elastic systems. The case $\alpha \in (0, \frac{1}{2})$, Proc. American Math. Soc., 110 (1989), 401405. doi: 10.2307/2048084. 
[5] 
U. Frisch, "Wave Propagation in Random Media, Probabilistic Methods in Applied Mathematics," I, 75198, Academic press, NewYork 1968. 
[6] 
K. Masuda, Manuscript for seminar at Kyoto University, 1970. 
[7] 
M. Ôtani, $L^\infty$energy method and its applications, in "Nonlinear Partial Differential Equations and Their Applications" (Ed. by N. Kenmochi, M. Ôtani and S. Zheng ), GAKUTO Internat. Ser. Math. Sci. Appl., 20, Gakkotosho, Tokyo, (2004), 505516. 
[8] 
M. Ôtani, $L^\infty$energy method, basic tools and usage, in "Differential Equations, Chaos and Variational Problems: Progress in Nonlinear Differential Equations and Their Applications" (Ed. by Vasile Staicu), 75, Birkhauser (2007), 357376. doi: 10.1007/9783764384821_27. 
[9] 
A. Pazy, "SemiGroups of Linear Operators and Applications to PDE," Applied Mathematical Science 44, Springer 1983. 
[10] 
H. B. Stewart, Generation of analytic semigroups by strongly elliptic operators, Trans.A.M.S., 199 (1974), 141162. 
show all references
References:
[1] 
T. Cazenave and A. Haraux, "An Introduction to Semilinear Evolution Equations," Oxford Lecture Series in Mathematics and its Applications, 13, 1998. 
[2] 
G. Chen and D. L. Russell, A mathematical model for linear elastic systems with structural damping, Quart. Appl. Math., 39 (1981/82), 433454. 
[3] 
S. Chen and R. Triggiani, Proof of extension of two conjectures on structural damping for elastic systems: The case $\frac{1}{2} \le\alpha\le 1$, Pacific. J. Math., 136 (1989), 1555. 
[4] 
S. Chen and R. Triggiani, Gevrey class semigroups arising from elastic systems. The case $\alpha \in (0, \frac{1}{2})$, Proc. American Math. Soc., 110 (1989), 401405. doi: 10.2307/2048084. 
[5] 
U. Frisch, "Wave Propagation in Random Media, Probabilistic Methods in Applied Mathematics," I, 75198, Academic press, NewYork 1968. 
[6] 
K. Masuda, Manuscript for seminar at Kyoto University, 1970. 
[7] 
M. Ôtani, $L^\infty$energy method and its applications, in "Nonlinear Partial Differential Equations and Their Applications" (Ed. by N. Kenmochi, M. Ôtani and S. Zheng ), GAKUTO Internat. Ser. Math. Sci. Appl., 20, Gakkotosho, Tokyo, (2004), 505516. 
[8] 
M. Ôtani, $L^\infty$energy method, basic tools and usage, in "Differential Equations, Chaos and Variational Problems: Progress in Nonlinear Differential Equations and Their Applications" (Ed. by Vasile Staicu), 75, Birkhauser (2007), 357376. doi: 10.1007/9783764384821_27. 
[9] 
A. Pazy, "SemiGroups of Linear Operators and Applications to PDE," Applied Mathematical Science 44, Springer 1983. 
[10] 
H. B. Stewart, Generation of analytic semigroups by strongly elliptic operators, Trans.A.M.S., 199 (1974), 141162. 
[1] 
Yoshinori Morimoto, ChaoJiang Xu. Analytic smoothing effect for the nonlinear Landau equation of Maxwellian molecules. Kinetic and Related Models, 2020, 13 (5) : 951978. doi: 10.3934/krm.2020033 
[2] 
Uchida Hidetake. Analytic smoothing effect and global existence of small solutions for the elliptichyperbolic DaveyStewartson system. Conference Publications, 2001, 2001 (Special) : 182190. doi: 10.3934/proc.2001.2001.182 
[3] 
Jeremy LeCrone, Gieri Simonett. Continuous maximal regularity and analytic semigroups. Conference Publications, 2011, 2011 (Special) : 963970. doi: 10.3934/proc.2011.2011.963 
[4] 
Yoshinori Morimoto, Karel PravdaStarov, ChaoJiang Xu. A remark on the ultraanalytic smoothing properties of the spatially homogeneous Landau equation. Kinetic and Related Models, 2013, 6 (4) : 715727. doi: 10.3934/krm.2013.6.715 
[5] 
Noboru Okazawa, Tomomi Yokota. Smoothing effect for generalized complex GinzburgLandau equations in unbounded domains. Conference Publications, 2001, 2001 (Special) : 280288. doi: 10.3934/proc.2001.2001.280 
[6] 
Lassaad Aloui, Imen El Khal El Taief. The Kato smoothing effect for the nonlinear regularized Schrödinger equation on compact manifolds. Mathematical Control and Related Fields, 2020, 10 (4) : 699714. doi: 10.3934/mcrf.2020016 
[7] 
Khaled El Dika. Smoothing effect of the generalized BBM equation for localized solutions moving to the right. Discrete and Continuous Dynamical Systems, 2005, 12 (5) : 973982. doi: 10.3934/dcds.2005.12.973 
[8] 
Burcu Özçam, Hao Cheng. A discretization based smoothing method for solving semiinfinite variational inequalities. Journal of Industrial and Management Optimization, 2005, 1 (2) : 219233. doi: 10.3934/jimo.2005.1.219 
[9] 
John Franks, Michael Handel. Some virtually abelian subgroups of the group of analytic symplectic diffeomorphisms of a surface. Journal of Modern Dynamics, 2013, 7 (3) : 369394. doi: 10.3934/jmd.2013.7.369 
[10] 
Joachim Escher, Rossen Ivanov, Boris Kolev. Euler equations on a semidirect product of the diffeomorphisms group by itself. Journal of Geometric Mechanics, 2011, 3 (3) : 313322. doi: 10.3934/jgm.2011.3.313 
[11] 
WeiXi Li, Lvqiao Liu. GelfandShilov smoothing effect for the spatially inhomogeneous Boltzmann equations without cutoff. Kinetic and Related Models, 2020, 13 (5) : 10291046. doi: 10.3934/krm.2020036 
[12] 
Olivier Goubet. Asymptotic smoothing effect for weakly damped forced Kortewegde Vries equations. Discrete and Continuous Dynamical Systems, 2000, 6 (3) : 625644. doi: 10.3934/dcds.2000.6.625 
[13] 
Hongjie Dong. Dissipative quasigeostrophic equations in critical Sobolev spaces: Smoothing effect and global wellposedness. Discrete and Continuous Dynamical Systems, 2010, 26 (4) : 11971211. doi: 10.3934/dcds.2010.26.1197 
[14] 
Aiting Le, Chenyin Qian. Smoothing effect and wellposedness for 2D Boussinesq equations in critical Sobolev space. Discrete and Continuous Dynamical Systems  B, 2022 doi: 10.3934/dcdsb.2022057 
[15] 
Zhi Guo Feng, Kok Lay Teo, Volker Rehbock. A smoothing approach for semiinfinite programming with projected Newtontype algorithm. Journal of Industrial and Management Optimization, 2009, 5 (1) : 141151. doi: 10.3934/jimo.2009.5.141 
[16] 
Andrey Itkin, Dmitry Muravey. Semianalytic pricing of double barrier options with timedependent barriers and rebates at hit. Frontiers of Mathematical Finance, 2022, 1 (1) : 5379. doi: 10.3934/fmf.2021002 
[17] 
Claire Chavaudret, Stefano Marmi. Analytic linearization of a generalization of the semistandard map: Radius of convergence and Brjuno sum. Discrete and Continuous Dynamical Systems, 2022, 42 (7) : 30773101. doi: 10.3934/dcds.2022009 
[18] 
Li Ma, Lin Zhao. Regularity for positive weak solutions to semilinear elliptic equations. Communications on Pure and Applied Analysis, 2008, 7 (3) : 631643. doi: 10.3934/cpaa.2008.7.631 
[19] 
Yemin Chen. Analytic regularity for solutions of the spatially homogeneous LandauFermiDirac equation for hard potentials. Kinetic and Related Models, 2010, 3 (4) : 645667. doi: 10.3934/krm.2010.3.645 
[20] 
Houda Mokrani. Semilinear subelliptic equations on the Heisenberg group with a singular potential. Communications on Pure and Applied Analysis, 2009, 8 (5) : 16191636. doi: 10.3934/cpaa.2009.8.1619 
2021 Impact Factor: 1.169
Tools
Metrics
Other articles
by authors
[Back to Top]