# American Institute of Mathematical Sciences

April  2016, 9(2): 457-474. doi: 10.3934/dcdss.2016007

## A geological delayed response model for stratigraphic reconstructions

 1 LaSIE, UMR-CNRS 7356, Université de La Rochelle, Avenue Michel Crépeau, 17000 La Rochelle, France, France

Received  March 2015 Revised  October 2015 Published  March 2016

We are interested by a nonlinear single lithology diffusion model adapted from ideas originally developed by the Institut Français du Pétrole (IFP). The geological stratigraphic modeling has to describe transports of sediments, erosion and sedimentation processes by taking into account a limited weathering condition; the method by which the history of a sedimentary basin is revealed relies on knowledge of both initial and final data and can be generalized to multiple lithology. For this purpose, we introduce a relaxation time related to a delayed response for establishing equilibrium states; this approach introduces regularizing effects according to the ideas of G.I. Barenblatt - S. Sobolev and J.-L. Lions - O. A. Oleinik. New well-posedness results are presented.
Citation: Gérard Gagneux, Olivier Millet. A geological delayed response model for stratigraphic reconstructions. Discrete & Continuous Dynamical Systems - S, 2016, 9 (2) : 457-474. doi: 10.3934/dcdss.2016007
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