Results 1  10
of
703,752
Weak solutions to a nonlinear variational wave equation with general data
 Annals of Inst. H. Poincaré
"... We establish the existence of a conservative weak solution to the Cauchy problem for the nonlinear variational wave equation utt − c(u)(c(u)ux)x = 0, for initial data of finite energy. Here c(·) is any smooth function with uniformly positive bounded values. ..."
Abstract

Cited by 17 (9 self)
 Add to MetaCart
We establish the existence of a conservative weak solution to the Cauchy problem for the nonlinear variational wave equation utt − c(u)(c(u)ux)x = 0, for initial data of finite energy. Here c(·) is any smooth function with uniformly positive bounded values.
Global Conservative Solutions to a Nonlinear Variational Wave Equation
, 2008
"... We establish the existence of a conservative weak solution to the Cauchy problem for the nonlinear variational wave equation utt − c(u)(c(u)ux)x = 0, for initial data of finite energy. Here c(·) is any smooth function with uniformly positive bounded values. ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
We establish the existence of a conservative weak solution to the Cauchy problem for the nonlinear variational wave equation utt − c(u)(c(u)ux)x = 0, for initial data of finite energy. Here c(·) is any smooth function with uniformly positive bounded values.
GLOBAL SEMIGROUP OF CONSERVATIVE SOLUTIONS OF THE NONLINEAR VARIATIONAL WAVE EQUATION
"... Abstract. We prove the existence of a global semigroup for conservative solutions of the nonlinear variational wave equation utt − c(u)(c(u)ux)x = 0. We allow for initial data ut=0 and utt=0 that contain measures. We assume that 0 < κ −1 ≤ c(u) ≤ κ. Solutions of this equation may experience con ..."
Abstract

Cited by 6 (0 self)
 Add to MetaCart
Abstract. We prove the existence of a global semigroup for conservative solutions of the nonlinear variational wave equation utt − c(u)(c(u)ux)x = 0. We allow for initial data ut=0 and utt=0 that contain measures. We assume that 0 < κ −1 ≤ c(u) ≤ κ. Solutions of this equation may experience
A CONVERGENT FINITE DIFFERENCE METHOD FOR A NONLINEAR VARIATIONAL WAVE EQUATION
"... Abstract. We establish rigorously convergence of a semidiscrete upwind scheme for the nonlinear variational wave equation utt − c(u)(c(u)ux)x = 0 with ut=0 = u0 and utt=0 = v0. Introducing Riemann invariants R = ut + cux and S = ut − cux, the variational wave equation is equivalent to Rt − cRx = ..."
Abstract
 Add to MetaCart
Abstract. We establish rigorously convergence of a semidiscrete upwind scheme for the nonlinear variational wave equation utt − c(u)(c(u)ux)x = 0 with ut=0 = u0 and utt=0 = v0. Introducing Riemann invariants R = ut + cux and S = ut − cux, the variational wave equation is equivalent to Rt − c
ROBUST FINITE DIFFERENCE SCHEMES FOR A NONLINEAR VARIATIONAL WAVE EQUATION MODELING LIQUID CRYSTALS
"... Abstract. We consider a nonlinear variational wave equation that models the dynamics of nematic liquid crystals. Finite difference schemes, that either conserve or dissipate a discrete version of the energy, associated with these equations, are designed. Numerical experiments, in both one and twosp ..."
Abstract
 Add to MetaCart
Abstract. We consider a nonlinear variational wave equation that models the dynamics of nematic liquid crystals. Finite difference schemes, that either conserve or dissipate a discrete version of the energy, associated with these equations, are designed. Numerical experiments, in both one and two
LOCAL DISCONTINUOUS GALERKIN SCHEMES FOR A NONLINEAR VARIATIONAL WAVE EQUATION MODELING LIQUID CRYSTALS
"... Abstract. We consider a nonlinear variational wave equation that models the dynamics of nematic liquid crystals. Discontinuous Galerkin schemes that either conserve or dissipate a discrete version of the energy associated with these equations are designed. Numerical experiments illustrating the sta ..."
Abstract
 Add to MetaCart
Abstract. We consider a nonlinear variational wave equation that models the dynamics of nematic liquid crystals. Discontinuous Galerkin schemes that either conserve or dissipate a discrete version of the energy associated with these equations are designed. Numerical experiments illustrating
Representation of dissipative solutions to a nonlinear variational wave equation
 Comm. Math. Sci
"... The paper introduces a new way to construct dissipative solutions to a second order variational wave equation. By a variable transformation, from the nonlinear PDE one obtains a semilinear hyperbolic system with sources. In contrast with the conservative case, here the source terms are discontinuou ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
The paper introduces a new way to construct dissipative solutions to a second order variational wave equation. By a variable transformation, from the nonlinear PDE one obtains a semilinear hyperbolic system with sources. In contrast with the conservative case, here the source terms
Nonlinear total variation based noise removal algorithms
, 1992
"... A constrained optimization type of numerical algorithm for removing noise from images is presented. The total variation of the image is minimized subject to constraints involving the statistics of the noise. The constraints are imposed using Lagrange multipliers. The solution is obtained using the g ..."
Abstract

Cited by 2270 (52 self)
 Add to MetaCart
A constrained optimization type of numerical algorithm for removing noise from images is presented. The total variation of the image is minimized subject to constraints involving the statistics of the noise. The constraints are imposed using Lagrange multipliers. The solution is obtained using
An introduction to variational methods for graphical models
 TO APPEAR: M. I. JORDAN, (ED.), LEARNING IN GRAPHICAL MODELS
"... ..."
Results 1  10
of
703,752