Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

This paper deals with the fractional Sobolev spaces W s;p . We analyze the relations among some of their possible denitions and their role in the trace theory. We prove continuous and compact embeddings, investigating the problem of the extension domains and other regularity results. Most of the results we present here are probably well known to the experts, but we believe that our proofs are original and we do not make use of any interpolation techniques nor pass through the theory of Besov spaces. We also present some counterexamples in non-Lipschitz domains.

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Hitchhiker's guide to the fractional Sobolev spaces

关于Semigroups of Linear Operators and Applications to Partial Differential Equations的两个注解

Singular Integral Equations. By N.I. Muskhelishvili. Translated fromthe 2nd Russian edition by J.R.M. Radok. Pp. 447. F1. 28.50. 1953. (Noordhoff, Groningen)

/pdf/introduction-to-the-modern-theory-of-dynamical-systems-1eced70mum.pdf

Introduction to the Modern Theory of Dynamical Systems

This paper is about one-dimensional symmetry properties for some entire and bounded solutions of ∆u + f(u) = 0 in IR. We consider solutions u such that −1 < u < 1 and u(x1, · · · , xn) → ±1 as xn → ±∞, uniformly with respect to x1, · · · , xn−1. Under some conditions on f , we prove that the solutions only depend on the variable xn. We also discuss more general elliptic operators. The qualitative properties then strongly depend on the coefficients of the operator. These results extend to higher dimensions and to more general operators a result of Ghoussoub and Gui [21] proved for n ≤ 3. AMS Classification : 35B05, 35B40, 35B50, 35J60.

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One-dimensional symmetry of bounded entire solutions of some elliptic equations

Travelling fronts with conical-shaped level sets are constructed for reaction-diffusion equations with bistable nonlinearities of positive mass The construction is valid in space dimension 2, where two proofs are given, and in arbitrary space dimensions under the assumption of cylindrical symmetry General qualitative properties are presented under various assumptions: conical conditions at infinity, existence of a sub-level set with globally Lipschitz boundary, monotonicity in a given direction

https://hal.archives-ouvertes.fr/hal-00003745/document

Existence and qualitative properties of multidimensional conical bistable fronts

This paper is concerned with the study of a model case of first order Hamilton-Jacobi equations posed on a ''junction'', that is to say the union of a finite number of half-lines with a unique common point. The main result is a comparison principle. We also prove existence and stability of solutions. The two challenging difficulties are the singular geometry of the domain and the discontinuity of the Hamiltonian. As far as discontinuous Hamiltonians are concerned, these results seem to be new. They are applied to the study of some models arising in traffic flows. The techniques developed in the present article provide new powerful tools for the analysis of such problems.

/pdf/a-hamilton-jacobi-approach-to-junction-problems-and-3dwfw04ei3.pdf

A Hamilton-Jacobi approach to junction problems and application to traffic flows

We study a nonlinear pseudodifferential equation describing the dynamics of dislocations in crystals. The long time asymptotics of solutions is described by the self-similar profiles.

/pdf/nonlinear-diffusion-of-dislocation-density-and-self-similar-52to9xv9kg.pdf

Nonlinear Diffusion of Dislocation Density and Self-Similar Solutions

We study a mathematical model describing dislocation dynamics in crystals. We consider a single dislocation line moving in its slip plane. The normal velocity is given by the Peach-Koehler force created by the dislocation line itself. The mathematical model is an eikonal equation with a velocity which is a non-local quantity depending on the whole shape of the dislocation line. We study the special case where the dislocation line is assumed to be a graph or a closed loop. In the framework of discontinuous viscosity solutions for Hamilton–Jacobi equations, we prove the existence and uniqueness of a solution for small time. We also give physical explanations and a formal derivation of the mathematical model. Finally, we present numerical results based on a level-sets formulation of the problem. These results illustrate in particular the fact that there is no general inclusion principle for this model.

/pdf/dislocation-dynamics-short-time-existence-and-uniqueness-of-2i4tt1bqm5.pdf

Régis Monneau

Papers

One-dimensional symmetry of bounded entire solutions of some elliptic equations

Existence and qualitative properties of multidimensional conical bistable fronts

A Hamilton-Jacobi approach to junction problems and application to traffic flows

Nonlinear Diffusion of Dislocation Density and Self-Similar Solutions

Dislocation Dynamics: Short-time Existence and Uniqueness of the Solution