H-measures and variants applied to parabolic equations

Journal of Mathematical Analysis and Applications

Volumn 343, Issue 1, 2008, Pages 207-225

  Antonić, Nenad ^a   Lazar, Martin ^a  

^a UNIVERSITY OF ZAGREB   (Croatia)

Author keywords

H measures; Oscillations; Parabolic equation; Schr dinger's equation

Indexed keywords

EID: 41449099286     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2007.12.077     Document Type: Article

References (18)

1. Antonić N. H-measures applied to symmetric systems. Proc. Roy. Soc. Edinburgh Sect. A 126 (1996) 1133-1155
2. Antonić N., and Lazar M. Microlocal energy density for hyperbolic systems. In: Drmač Z., et al. (Ed). Applied Mathematics and Scientific Computing (2003), Kluwer Academic/Plenum Publishers 179-190
3. Nenad Antonić, Martin Lazar, Parabolic variant of H-measures in homogenisation of a model problem based on Navier-Stokes equation, submitted for publication
4. Nenad Antonić, Martin Lazar, An application of parabolic variant of H-measures, submitted for publication
5. Balakrishnan A.V. Applied Functional Analysis (1976), Springer
6. Bensoussan A., Lions J.L., and Papanicolaou G. Asymptotic Analysis for Periodic Structures (1978), North-Holland
7. Dautray R., and Lions J.L. Mathematical Analysis and Numerical Methods for Science and Technology, vols. 1-6 (1992), Springer
8. Dall'Aglio A., and Murat F. A corrector result for H-converging parabolic problems with time-dependent coefficients. Ann. Sc. Norm. Super. Pisa Cl. Sci. (4) 25 (1997) 329-373
9. Francfort G.A. An introduction to H-measures and their applications. Variational Problems in Materials Science. Progr. Nonlinear Differential Equations Appl. vol. 68 (2006), Birkhäuser 85-110
10. Francfort G.A., and Murat F. Oscillations and energy densities in the wave equation. Comm. Partial Differential Equations 17 (1992) 1785-1865
11. Gérard P. Microlocal defect measures. Comm. Partial Differential Equations 16 (1991) 1761-1794
12. Gérard P. Oscillations and concentration effects in semilinear dispersive wave equations. J. Funct. Anal. 141 (1996) 60-98
13. Gilbarg D., and Trudinger N.S. Elliptic Partial Differential Equations of Second Order (1983), Springer
14. Hörmander L. The Analysis of Linear Partial Differential Operators I-IV (1983-1985), Springer
15. Saint-Raymond X. Elementary Introduction to the Theory of Pseudodifferential Operators (1991), CRC Press
16. Tartar L. H-measures, a new approach for studying homogenisation, oscillations and concentration effects in partial differential equations. Proc. Roy. Soc. Edinburgh Sect. A 115 (1990) 193-230
17. Tartar L. Mathematical tools for studying oscillations and concentrations: From Young measures to H-measures and their variants. In: Antonić N., et al. (Ed). Multiscale Problems in Science and Technology (2002), Springer 1-84
18. Trèves F. Introduction to Pseudodifferential and Fourier Integral Operators I-II (1980), Plenum Press