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Applicable Analysis
An International Journal
Volume 88, 2009 - Issue 10-11: Mathematical Modelling and Numerical Simulation of Flow and Transport in Porous Media
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Original Articles

Parabolic H-convergence and small-amplitude homogenization

Nenad Antonić Department of Mathematics, University of Zagreb, Bijenička cesta 30, Zagreb, Croatia
&
Marko Vrdoljak Department of Mathematics, University of Zagreb, Bijenička cesta 30, Zagreb, CroatiaCorrespondence[email protected]
Pages 1493-1508 | Received 26 Jan 2009, Accepted 08 May 2009, Published online: 17 Nov 2009

References

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  • Colombini , F and Spagnolo , S . 1977 . Sur la convergence de solutions d'équations paraboliques . J. Math. Pure. Appl. , 56 : 263 – 306 .
  • Tartar , L . 1989 . “ H-measures and small amplitude homogenisation ” . In Random Media and Composites , Edited by: Kohn , R and Milton , G . 89 – 99 . Philadelphia : SIAM .
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  • Tartar , L . 2002 . “ Mathematical tools for studying oscillations and concentrations: from Young measures to H-measures and their variants ” . In Multiscale Problems in Science and Technology , Edited by: Antonić , N . 1 – 84 . Berlin : Springer .
  • Antonić , N and Vrdoljak , M . 2009 . Small-amplitude homogenisation of diffusion equation . Int. J. Pure Appl. Math. , 50 : 233 – 238 .
  • Kato , T . 1995 . Perturbation Theory for Linear Operators , New York : Springer .
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  • Antonić , N . 1996 . H-measures applied to symmetric systems . Proc. Roy. Soc. Edinburgh , 126A : 1133 – 1155 .
  • Antonić , N and Lazar , M . Parabolic variant of H-measures in homogenisation of a model problem based on Navier-Stokes equation . Nonlinear Anal., Real World Appl. (to appear) ,
  • Bensoussan , A , Lions , J-L and Papanicolaou , G . 1978 . Asymptotic Analysis for Periodic Structures , Amsterdam : North-Holland .

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