Abstract
We review recent results on homogenization of nonlinear partial differential equations in ergodic algebras. We describe some open problems concerning the general theory of with mean value (algebras w.m.v., in short). We also prove a new result establishing the invariance of any algebra w.m.v. under the flow of a Lipschitz continuous divergence-free vector field whose components belong to the corresponding algebra w.m.v., thus solving a problem left open by the authors in a previous paper.
H. Frid gratefully acknowledges the support of CNPq, grant 306137/2006-2, and FAPERJ, grant E-26/152.192-2002.
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Frid, H., Silva, J. (2011). Homogenization of Nonlinear Partial Differential Equations in the Context of Ergodic Algebras: Recent Results and Open Problems. In: Bressan, A., Chen, GQ., Lewicka, M., Wang, D. (eds) Nonlinear Conservation Laws and Applications. The IMA Volumes in Mathematics and its Applications, vol 153. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-9554-4_14
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DOI: https://doi.org/10.1007/978-1-4419-9554-4_14
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