Identifiabilité d'un coefficient variable en espace dans une équation parabolique
Implicit difference methods for quasilinear parabolic functional differential systems.
Implicit-explicit Runge–Kutta schemes and finite elements with symmetric stabilization for advection-diffusion equations
We analyze a two-stage implicit-explicit Runge–Kutta scheme for time discretization of advection-diffusion equations. Space discretization uses continuous, piecewise affine finite elements with interelement gradient jump penalty; discontinuous Galerkin methods can be considered as well. The advective and stabilization operators are treated explicitly, whereas the diffusion operator is treated implicitly. Our analysis hinges on L2-energy estimates on discrete functions in physical space. Our main...
Implicit-explicit Runge–Kutta schemes and finite elements with symmetric stabilization for advection-diffusion equations
We analyze a two-stage implicit-explicit Runge–Kutta scheme for time discretization of advection-diffusion equations. Space discretization uses continuous, piecewise affine finite elements with interelement gradient jump penalty; discontinuous Galerkin methods can be considered as well. The advective and stabilization operators are treated explicitly, whereas the diffusion operator is treated implicitly. Our analysis hinges on L2-energy estimates on discrete functions in physical space. Our main...
Implicit-explicit Runge–Kutta schemes and finite elements with symmetric stabilization for advection-diffusion equations
We analyze a two-stage implicit-explicit Runge–Kutta scheme for time discretization of advection-diffusion equations. Space discretization uses continuous, piecewise affine finite elements with interelement gradient jump penalty; discontinuous Galerkin methods can be considered as well. The advective and stabilization operators are treated explicitly, whereas the diffusion operator is treated implicitly. Our analysis hinges on L2-energy estimates on discrete functions in physical space. Our main...
Impulsive nonlocal nonlinear parabolic differential problems.
Inhomogeneous parabolic Neumann problems
Second order parabolic equations on Lipschitz domains subject to inhomogeneous Neumann (or, more generally, Robin) boundary conditions are studied. Existence and uniqueness of weak solutions and their continuity up to the boundary of the parabolic cylinder are proved using methods from the theory of integrated semigroups, showing in particular the well-posedness of the abstract Cauchy problem in spaces of continuous functions. Under natural assumptions on the coefficients and the inhomogeneity the...
Initial-boundary value problems in a plane corner for the heat equation.
Internal exact controllability of the linear population dynamics with diffusion.
Invariant wedges for a two-point reflecting Brownian motion and the “hot spots” problem.
Invertibility of some heat potentials in norms
Isoperimetric inequalities in parabolic equations
Iterative methods for parabolic functional differential equations
This paper is concerned with iterative methods for parabolic functional differential equations with initial boundary conditions. Monotone iterative methods are discussed. We prove a theorem on the existence of solutions for a parabolic problem whose right-hand side admits a Jordan type decomposition with respect to the function variable. It is shown that there exist Newton sequences which converge to the solution of the initial problem. Differential equations with deviated variables and differential...