
Previous Article
Asymptotic behaviour of a nonautonomous population equation with diffusion in $L^1$
 DCDS Home
 This Issue

Next Article
On two noteworthy deformations of negatively curved Riemannian metrics
Pazytype characterization for differentiability of propagators of higher order Cauchy problems in Banach spaces
1.  Department of Mathematics, University of Science and Technology of China, Hefei 230026, China, China 
$u^{(n)}(t) +\sum_{k=0}^{n1}A_ku^{(k)}(t)=0, t\geq 0,$
$u^{(k)}(0) = u_k, 0\leq k\leq n1,
where $A_0, A_1,\ldots, A_{n1}$ are densely defined closed linear operators on a Banach space. A Pazytype characterization of the infinitely differentiable propagators of the Cauchy problem is obtained. Moreover, two related sufficient conditions are given.
[1] 
Doria Affane, Mustapha Fateh Yarou. Wellposed control problems related to secondorder differential inclusions. Evolution Equations and Control Theory, 2022, 11 (4) : 12291249. doi: 10.3934/eect.2021042 
[2] 
Belkacem SaidHouari. Global wellposedness of the Cauchy problem for the Jordan–Moore–Gibson–Thompson equation with arbitrarily large higherorder Sobolev norms. Discrete and Continuous Dynamical Systems, 2022, 42 (9) : 46154635. doi: 10.3934/dcds.2022066 
[3] 
Feng Wang, Fengquan Li, Zhijun Qiao. On the Cauchy problem for a higherorder μCamassaHolm equation. Discrete and Continuous Dynamical Systems, 2018, 38 (8) : 41634187. doi: 10.3934/dcds.2018181 
[4] 
Feliz Minhós, Rui Carapinha. On higher order nonlinear impulsive boundary value problems. Conference Publications, 2015, 2015 (special) : 851860. doi: 10.3934/proc.2015.0851 
[5] 
T. J. Sullivan. Wellposed Bayesian inverse problems and heavytailed stable quasiBanach space priors. Inverse Problems and Imaging, 2017, 11 (5) : 857874. doi: 10.3934/ipi.2017040 
[6] 
Jon Johnsen. Wellposed final value problems and Duhamel's formula for coercive Lax–Milgram operators. Electronic Research Archive, 2019, 27: 2036. doi: 10.3934/era.2019008 
[7] 
W. Layton, R. Lewandowski. On a wellposed turbulence model. Discrete and Continuous Dynamical Systems  B, 2006, 6 (1) : 111128. doi: 10.3934/dcdsb.2006.6.111 
[8] 
Shouming Zhou. The Cauchy problem for a generalized $b$equation with higherorder nonlinearities in critical Besov spaces and weighted $L^p$ spaces. Discrete and Continuous Dynamical Systems, 2014, 34 (11) : 49674986. doi: 10.3934/dcds.2014.34.4967 
[9] 
Huijun He, Zhaoyang Yin. On the Cauchy problem for a generalized twocomponent shallow water wave system with fractional higherorder inertia operators. Discrete and Continuous Dynamical Systems, 2017, 37 (3) : 15091537. doi: 10.3934/dcds.2017062 
[10] 
Mohammad Kafini. On the blowup of the Cauchy problem of higherorder nonlinear viscoelastic wave equation. Discrete and Continuous Dynamical Systems  S, 2022, 15 (5) : 12211232. doi: 10.3934/dcdss.2021093 
[11] 
Rinaldo M. Colombo, Mauro Garavello. A Well Posed Riemann Problem for the $p$System at a Junction. Networks and Heterogeneous Media, 2006, 1 (3) : 495511. doi: 10.3934/nhm.2006.1.495 
[12] 
Simão P. S. Santos, Natália Martins, Delfim F. M. Torres. Noether's theorem for higherorder variational problems of Herglotz type. Conference Publications, 2015, 2015 (special) : 990999. doi: 10.3934/proc.2015.990 
[13] 
John Baxley, Mary E. Cunningham, M. Kathryn McKinnon. Higher order boundary value problems with multiple solutions: examples and techniques. Conference Publications, 2005, 2005 (Special) : 8490. doi: 10.3934/proc.2005.2005.84 
[14] 
Carlos Durán, Diego Otero. The projective symplectic geometry of higher order variational problems: Minimality conditions. Journal of Geometric Mechanics, 2016, 8 (3) : 305322. doi: 10.3934/jgm.2016009 
[15] 
Feliz Minhós, A. I. Santos. Higher order twopoint boundary value problems with asymmetric growth. Discrete and Continuous Dynamical Systems  S, 2008, 1 (1) : 127137. doi: 10.3934/dcdss.2008.1.127 
[16] 
Leonardo Colombo, David Martín de Diego. Higherorder variational problems on lie groups and optimal control applications. Journal of Geometric Mechanics, 2014, 6 (4) : 451478. doi: 10.3934/jgm.2014.6.451 
[17] 
Yuanyuan Ren, Yongsheng Li, Wei Yan. Sharp wellposedness of the Cauchy problem for the fourth order nonlinear Schrödinger equation. Communications on Pure and Applied Analysis, 2018, 17 (2) : 487504. doi: 10.3934/cpaa.2018027 
[18] 
G. R. Cirmi, S. Leonardi. Higher differentiability for solutions of linear elliptic systems with measure data. Discrete and Continuous Dynamical Systems, 2010, 26 (1) : 89104. doi: 10.3934/dcds.2010.26.89 
[19] 
Mikil Foss, Joe Geisbauer. Higher differentiability in the context of Besov spaces for a class of nonlocal functionals. Evolution Equations and Control Theory, 2013, 2 (2) : 301318. doi: 10.3934/eect.2013.2.301 
[20] 
Hongqiu Chen. Wellposedness for a higherorder, nonlinear, dispersive equation on a quarter plane. Discrete and Continuous Dynamical Systems, 2018, 38 (1) : 397429. doi: 10.3934/dcds.2018019 
2021 Impact Factor: 1.588
Tools
Metrics
Other articles
by authors
[Back to Top]