Stationary quasi-P eikonal equations, stationary Hamilton-Jacobi equations, arise from the asymptotic approximation of anisotropic wave propagation. A paraxial formulation of the quasi-P eikonal equation results in a paraxial quasi-P eikonal equation, an evolution Hamilton-Jacobi equation in a preferred direction, which provides a fast and efficient way for computing viscosity solutions of quas...

The Shape–from–Shading models in image analysis lead to first order Hamilton– Jacobi equations which may have several weak solutions (in the viscosity sense). Moreover, for real images, these equations are highly discontinuous in the space variable. The lack of uniqueness and the irregularity of the coefficients involve some troubles when we try to compute a solution. In order to avoid these di...

We prove that viscosity solutions in W 1'~176 of the second order, fully nonlinear, equation F(D2u, Du, u) = 0 are unique when (i) F is degenerate elliptic and decreasing in u or (ii) Fis uniformly elliptic and nonincreasing in u. We do not assume that F is convex. The method of proof involves constructing nonlinear approximation operators which map viscosity subsolutions and supersolutions ont...

Artificial viscosity can be combined with a higher-order discontinuous Galerkin finite element discretization to resolve a shock layer within a single cell. However, when a non-smooth artificial viscosity model is employed with an otherwise higherorder approximation, element-to-element variations induce oscillations in state gradients and pollute the downstream flow. To alleviate these difficul...

We consider the (reaction-coordinate) viscosity dependence of reaction-rate coefficients for the two-dimensional AgmonKosloff surface. We show that rate coefficients calculated from the Agmon-Hopfield sink-Smoluchowski equation are a lower bound, approaching asymptotically the two-dimensional result for fast reactive-mode diffusion. A modified equation, employing an effective potential in the s...

In this paper we study an approximation scheme for a class of Hamilton-Jacobi problems for which uniqueness of the viscosity solution does not hold. This class includes the Eikonal equation arising in the Shape from Shading problem. We show that, if an appropriate stability condition is satissed, the scheme converges to the maximal viscosity solution of the problem. Furthermore we give an estim...

We present methodological innovations to the multi-component lattice Boltzmann equation simulation method which allow for the simulation of dynamic contact lines in the continuum approximation. The improvements are set-out and verified by quantitative results. They allow the simulator access to an expanded range of simulation parameters like viscosity, viscosity contrast and interfacial tension...

We prove a theorem of existence of time-optimal curves in the space of probability measures, a Dynamic Programming Principle, a controllability result and some comparisons between the classical and the generalized framework. A proper definition of viscosity solution, together with some approximation results, leaded us to prove that the generalization of the minimum time function solves a suitab...