Electron. J. Diff. Eqns., Vol. 2001(2001), No. 17, pp. 1-19.

Homogenization of a nonlinear degenerate parabolic differential equation

A. K. Nandakumaran & M. Rajesh

Abstract:
In this article, we study the homogenization of the nonlinear degenerate parabolic equation
$$ \partial_t b({x /over \varepsilon},u_\varepsilon) - \mathop{\rm div} a({x /over \varepsilon},{t \over \varepsilon}, u_\varepsilon,\nabla u_\varepsilon)=f(x,t), $$
with mixed boundary conditions(Neumann and Dirichlet) and obtain the limit equation as $\varepsilon \to 0$. We also prove corrector results to improve the weak convergence of $\nabla u_\varepsilon$ to strong convergence.

Submitted September 11, 2000. Published March 15, 2001.
Math Subject Classifications: 35B27, 74Q10.
Key Words: degenerate parabolic equation, homogenization, two-scale convergence, correctors.

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A. K. Nandakumaran
Department of Mathematics
Indian Institute of Science
Bangalore- 560 012, India
e-mail: nands@math.iisc.ernet.in
M. Rajesh
Department of Mathematics
Indian Institute of Science
Bangalore- 560 012, India
e-mail: rajesh@math.iisc.ernet.in

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