-
Previous Article
On the central stability zone for linear discrete-time Hamiltonian systems
- PROC Home
- This Issue
-
Next Article
Exponential attractor for the delayed logistic equation with a nonlinear diffusion
Parabolic systems with non continuous coefficients
| 1. | Dipartimento di Matematica e Informatica, Viale Andrea Doria, 6, 95128- Catania, Italy |
$T u = fi(y)$ $i = 1,...,N
where the known terms $f_i$ are in Lebesgue spaces and the differential the parabolic operator $T$ has the form
$ut - \sum_{j=1}^{N}\sum_{|\alpha|=2s} a^(\alpha)_(ij) (y)D^(\alpha) u_j (y) + \sum_{j=1}^{N}\sum_{|\alpha|<=2s-1} b^(\alpha)_(ij) (y)D^(\alpha) u_j (y)$.
have discontinuous coefficients.
| [1] |
Denis R. Akhmetov, Renato Spigler. $L^1$-estimates for the higher-order derivatives of solutions to parabolic equations subject to initial values of bounded total variation. Communications on Pure & Applied Analysis, 2007, 6 (4) : 1051-1074. doi: 10.3934/cpaa.2007.6.1051 |
| [2] |
Kai Liu. Stationary solutions of neutral stochastic partial differential equations with delays in the highest-order derivatives. Discrete & Continuous Dynamical Systems - B, 2018, 23 (9) : 3915-3934. doi: 10.3934/dcdsb.2018117 |
| [3] |
Jie Jiang. Global stability of Keller–Segel systems in critical Lebesgue spaces. Discrete & Continuous Dynamical Systems - A, 2020, 40 (1) : 609-634. doi: 10.3934/dcds.2020025 |
| [4] |
Marina V. Plekhanova. Strong solutions of quasilinear equations in Banach spaces not solvable with respect to the highest-order derivative. Discrete & Continuous Dynamical Systems - S, 2016, 9 (3) : 833-846. doi: 10.3934/dcdss.2016031 |
| [5] |
Xuanji Jia, Yong Zhou. Regularity criteria for the 3D MHD equations via partial derivatives. II. Kinetic & Related Models, 2014, 7 (2) : 291-304. doi: 10.3934/krm.2014.7.291 |
| [6] |
Julii A. Dubinskii. Complex Neumann type boundary problem and decomposition of Lebesgue spaces. Discrete & Continuous Dynamical Systems - A, 2004, 10 (1&2) : 201-210. doi: 10.3934/dcds.2004.10.201 |
| [7] |
Maria Alessandra Ragusa, Atsushi Tachikawa. Estimates of the derivatives of minimizers of a special class of variational integrals. Discrete & Continuous Dynamical Systems - A, 2011, 31 (4) : 1411-1425. doi: 10.3934/dcds.2011.31.1411 |
| [8] |
Dian Palagachev, Lubomira Softova. A priori estimates and precise regularity for parabolic systems with discontinuous data. Discrete & Continuous Dynamical Systems - A, 2005, 13 (3) : 721-742. doi: 10.3934/dcds.2005.13.721 |
| [9] |
Lijuan Wang, Jun Zou. Error estimates of finite element methods for parameter identifications in elliptic and parabolic systems. Discrete & Continuous Dynamical Systems - B, 2010, 14 (4) : 1641-1670. doi: 10.3934/dcdsb.2010.14.1641 |
| [10] |
Horst Heck, Matthias Hieber, Kyriakos Stavrakidis. $L^\infty$-estimates for parabolic systems with VMO-coefficients. Discrete & Continuous Dynamical Systems - S, 2010, 3 (2) : 299-309. doi: 10.3934/dcdss.2010.3.299 |
| [11] |
Thuy N. T. Nguyen. Uniform controllability of semidiscrete approximations for parabolic systems in Banach spaces. Discrete & Continuous Dynamical Systems - B, 2015, 20 (2) : 613-640. doi: 10.3934/dcdsb.2015.20.613 |
| [12] |
Weisheng Niu, Yao Xu. Convergence rates in homogenization of higher-order parabolic systems. Discrete & Continuous Dynamical Systems - A, 2018, 38 (8) : 4203-4229. doi: 10.3934/dcds.2018183 |
| [13] |
Shaohua Chen. Boundedness and blowup solutions for quasilinear parabolic systems with lower order terms. Communications on Pure & Applied Analysis, 2009, 8 (2) : 587-600. doi: 10.3934/cpaa.2009.8.587 |
| [14] |
Chao Deng, Tong Li. Global existence and large time behavior of a 2D Keller-Segel system in logarithmic Lebesgue spaces. Discrete & Continuous Dynamical Systems - B, 2019, 24 (1) : 183-195. doi: 10.3934/dcdsb.2018093 |
| [15] |
Hartmut Pecher. The Chern-Simons-Higgs and the Chern-Simons-Dirac equations in Fourier-Lebesgue spaces. Discrete & Continuous Dynamical Systems - A, 2019, 39 (8) : 4875-4893. doi: 10.3934/dcds.2019199 |
| [16] |
Yuri Latushkin, Valerian Yurov. Stability estimates for semigroups on Banach spaces. Discrete & Continuous Dynamical Systems - A, 2013, 33 (11&12) : 5203-5216. doi: 10.3934/dcds.2013.33.5203 |
| [17] |
Nobuyuki Kato, Norio Kikuchi. Campanato-type boundary estimates for Rothe's scheme to parabolic partial differential systems with constant coefficients. Discrete & Continuous Dynamical Systems - A, 2007, 19 (4) : 737-760. doi: 10.3934/dcds.2007.19.737 |
| [18] |
Zaihong Wang. Periodic solutions of the second order differential equations with asymmetric nonlinearities depending on the derivatives. Discrete & Continuous Dynamical Systems - A, 2003, 9 (3) : 751-770. doi: 10.3934/dcds.2003.9.751 |
| [19] |
Hongjie Dong, Seick Kim. Green's functions for parabolic systems of second order in time-varying domains. Communications on Pure & Applied Analysis, 2014, 13 (4) : 1407-1433. doi: 10.3934/cpaa.2014.13.1407 |
| [20] |
Kyeong-Hun Kim, Kijung Lee. A weighted $L_p$-theory for second-order parabolic and elliptic partial differential systems on a half space. Communications on Pure & Applied Analysis, 2016, 15 (3) : 761-794. doi: 10.3934/cpaa.2016.15.761 |
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]