Analysis of the self-similar solutions of a generalized Burgers equation with nonlinear damping.
Analysis of total variation flow and its finite element approximations
We study the gradient flow for the total variation functional, which arises in image processing and geometric applications. We propose a variational inequality weak formulation for the gradient flow, and establish well-posedness of the problem by the energy method. The main idea of our approach is to exploit the relationship between the regularized gradient flow (characterized by a small positive parameter , and the minimal surface flow [21] and the prescribed mean curvature flow [16]. Since our...
Analysis of total variation flow and its finite element approximations
We study the gradient flow for the total variation functional, which arises in image processing and geometric applications. We propose a variational inequality weak formulation for the gradient flow, and establish well-posedness of the problem by the energy method. The main idea of our approach is to exploit the relationship between the regularized gradient flow (characterized by a small positive parameter ε, see (1.7)) and the minimal surface flow [21] and the prescribed mean curvature flow [16]. Since...
Analysis tools for finite volume schemes
Analytic approach to systems in potential models.
Analytic solution of an initial-value problem from Stokes flow with free boundary.
Analytical and numerical methods for the CMKdV-II equation.
Analytical and numerical solutions to initial-boundary value problems of the water wave motion in a reservoir.
Analytical approximation of the transition density in a local volatility model
We present a simplified approach to the analytical approximation of the transition density related to a general local volatility model. The methodology is sufficiently flexible to be extended to time-dependent coefficients, multi-dimensional stochastic volatility models, degenerate parabolic PDEs related to Asian options and also to include jumps.
Analytical solution of a general boundary value problem for a BKW-equation.
Analytical solution of the hyperbolic heat conduction equation for moving semi-infinite medium under the effect of time-dependent laser heat source.
Analytical treatment of generalized Burgers-Huxley equation by homotopy analysis method.
Analyticité locale pour les solutions de l'équation d'Euler
Analyticity of solutions and Kolmogorov's dissipation scale for 2D Navier-Stokes equations
Analyticity of the interface in a free boundary problem.
Analyzing the dynamics of the forced Burgers equation.
Andrew Lenard: a mystery unraveled.
Anisotropic inverse problems and Carleman estimates
This note reports on recent results on the anisotropic Calderón problem obtained in a joint work with Carlos E. Kenig, Mikko Salo and Gunther Uhlmann [8]. The approach is based on the construction of complex geometrical optics solutions to the Schrödinger equation involving phases introduced in the work [12] of Kenig, Sjöstrand and Uhlmann in the isotropic setting. We characterize those manifolds where the construction is possible, and give applications to uniqueness for the corresponding anisotropic...
Anisotropic mesh adaption: application to computational fluid dynamics
In this communication we focus on goal-oriented anisotropic adaption techniques. Starting point has been the derivation of suitable anisotropic interpolation error estimates for piecewise linear finite elements, on triangular grids in . Then we have merged these interpolation estimates with the dual-based a posteriori error analysis proposed by R. Rannacher and R. Becker. As examples of this general anisotropic a posteriori analysis, elliptic, advection-diffusion-reaction and the Stokes problems...
Antieigenvalue analysis for continuum mechanics, economics, and number theory
My recent book Antieigenvalue Analysis, World-Scientific, 2012, presented the theory of antieigenvalues from its inception in 1966 up to 2010, and its applications within those forty-five years to Numerical Analysis, Wavelets, Statistics, Quantum Mechanics, Finance, and Optimization. Here I am able to offer three further areas of application: Continuum Mechanics, Economics, and Number Theory. In particular, the critical angle of repose in a continuum model of granular materials is shown to be exactly...