An existence theorem for semilinear functional parabolic equations
An explicit determination of the space-times on which the conformally invariant scalar wave equation satisfies Huygens' principle. — Part II : Petrov type D space-times
An explicit modified method of characteristics for the one-dimensional nonstationary convection-diffusion problem with dominating convection
We describe a numerical method for the equation in with Dirichlet boundary and initial conditions which is a combination of the method of characteristics and the finite-difference method. We prove both an a priori local error-estimate of a high order and stability. Example 3.3 indicates that our approximate solutions are disturbed only by a minimal amount of the artificial diffusion.
An extension of Rothe's method to non-cylindrical domains
In this paper Rothe’s classical method is extended so that it can be used to solve some linear parabolic boundary value problems in non-cylindrical domains. The corresponding existence and uniqueness theorems are proved and some further results and generalizations are discussed and applied.
An extension theorem for supertemperatures.
An -Galerkin method for a Stefan problem with a quasilinear parabolic equation in nondivergence form.
An IMEX scheme for reaction-diffusion equations: application for a PEM fuel cell model
An implicit-explicit (IMEX) method is developed for the numerical solution of reaction-diffusion equations with pure Neumann boundary conditions. The corresponding method of lines scheme with finite differences is analyzed: explicit conditions are given for its convergence in the ‖·‖∞ norm. The results are applied to a model for determining the overpotential in a proton exchange membrane (PEM) fuel cell.
An implicit method for fuzzy parabolic partial differential equations.
An implicit scheme to solve a system of ODEs arising from the space discretization of nonlinear diffusion equations
In this article, we consider the initial value problem which is obtained after a space discretization (with space step ) of the equations governing the solidification process of a multicomponent alloy. We propose a numerical scheme to solve numerically this initial value problem. We prove an error estimate which is not affected by the step size chosen in the space discretization. Consequently, our scheme provides global convergence without any stability condition between and the time step size...
An implicit scheme to solve a system of ODEs arising from the space discretization of nonlinear diffusion equations
In this article, we consider the initial value problem which is obtained after a space discretization (with space step h) of the equations governing the solidification process of a multicomponent alloy. We propose a numerical scheme to solve numerically this initial value problem. We prove an error estimate which is not affected by the step size h chosen in the space discretization. Consequently, our scheme provides global convergence without any stability condition between h and the time...
An index for global Hopf bifurcation in parabolic systems.
An inequality on solutions of heat equation.
An inertial manifold and the principle of spatial averaging.
An initial boundary value problem for Maxwell's equations in a parabolic limit case.
An initial-boundary value problem for quasi-linear parabolic systems of higher order
An Initial-Boundary-Value Problem for a Certain Density-Dependent Diffusion System.
An integrodifferential approach to modeling, control, state estimation and optimization for heat transfer systems
In this paper, control-oriented modeling approaches are presented for distributed parameter systems. These systems, which are in the focus of this contribution, are assumed to be described by suitable partial differential equations. They arise naturally during the modeling of dynamic heat transfer processes. The presented approaches aim at developing finitedimensional system descriptions for the design of various open-loop, closed-loop, and optimal control strategies as well as state, disturbance,...
An inverse eigenvalue problem for an arbitrary multiply connected bounded region: An extension to higher dimensions.
An inverse problem for evolution inclusions.
An inverse problem in a parabolic equation.