Remarks relevant to classical maximum principles.
Removable singularities of solutions of the heat equation with special growth
Renormalized entropy solutions for degenerate nonlinear evolution problems.
Renormalized solution for nonlinear degenerate problems in the whole space
We consider the general degenerate parabolic equation :We suppose that the flux is continuous, is nondecreasing continuous and both functions are not necessarily Lipschitz. We prove the existence of the renormalized solution of the associated Cauchy problem for initial data and source term. We establish the uniqueness of this type of solution under a structure condition and an assumption on the modulus of continuity of . The novelty of this work is that , , , , are not Lipschitz...
Renormalized solutions of a nonlinear parabolic equation with double degeneracy.
Representation theorems and Fatou theorems for parabolic systems in the sense of Petrovskiĭ
Résolution numérique du problème de propagation de la chaleur à une dimension par la méthode itérative de sur-relaxation
Resolvent estimates in for discrete Laplacians on irregular meshes and maximum-norm stability of parabolic finite difference schemes.
Resolvent estimates of elliptic differential and finite-element operators in pairs of function spaces.
Resolvent positive operators and inhomogeneous boundary conditions
Results on existence of solution for an optimal design problem.
In this paper we study a control problem for elliptic nonlinear monotone problems with Dirichlet boundary conditions where the control variables are the coefficients of the equation and the open set where the partial differential problem is studied.
Reverse convolution inequalities and applications to inverse heat source problems.
Reverse smoothing effects, fine asymptotics, and Harnack inequalities for fast diffusion equations.
Riesz transform on manifolds and heat kernel regularity
Rigorous numerics for the Cahn-Hilliard equation on the unit square.
Ritz Approximations to Two-Dimensional Boundary Value Problems.
Robust a posteriori error estimates for finite element discretizations of the heat equation with discontinuous coefficients
In this work we derive a posteriori error estimates based on equations residuals for the heat equation with discontinuous diffusivity coefficients. The estimates are based on a fully discrete scheme based on conforming finite elements in each time slab and on the A-stable -scheme with . Following remarks of [Picasso, Comput. Methods Appl. Mech. Engrg. 167 (1998) 223–237; Verfürth, Calcolo 40 (2003) 195–212] it is easy to identify a time-discretization error-estimator and a space-discretization...
Robust a posteriori error estimates for finite element discretizations of the heat equation with discontinuous coefficients
In this work we derive a posteriori error estimates based on equations residuals for the heat equation with discontinuous diffusivity coefficients. The estimates are based on a fully discrete scheme based on conforming finite elements in each time slab and on the A-stable θ-scheme with 1/2 ≤ θ ≤ 1. Following remarks of [Picasso, Comput. Methods Appl. Mech. Engrg. 167 (1998) 223–237; Verfürth, Calcolo40 (2003) 195–212] it is easy to identify a time-discretization error-estimator and a space-discretization...
Robust a priori error analysis for the approximation of degree-one Ginzburg-Landau vortices
This article discusses the numerical approximation of time dependent Ginzburg-Landau equations. Optimal error estimates which are robust with respect to a large Ginzburg-Landau parameter are established for a semi-discrete in time and a fully discrete approximation scheme. The proofs rely on an asymptotic expansion of the exact solution and a stability result for degree-one Ginzburg-Landau vortices. The error bounds prove that degree-one vortices can be approximated robustly while unstable higher...
Robust a priori error analysis for the approximation of degree-one Ginzburg-Landau vortices
This article discusses the numerical approximation of time dependent Ginzburg-Landau equations. Optimal error estimates which are robust with respect to a large Ginzburg-Landau parameter are established for a semi-discrete in time and a fully discrete approximation scheme. The proofs rely on an asymptotic expansion of the exact solution and a stability result for degree-one Ginzburg-Landau vortices. The error bounds prove that degree-one vortices can be approximated robustly while unstable higher...