Fundamental Research and Applied Numerical Analysis in Partial Differential Equations and Functional Partial Differential Equations

点击翻译按钮获取中文摘要

1. The property of Semi-Fredholm operators are effectively applied to the existence of periodic solutions of linear, nonhomogeneous functional differential equations described by the noncompact operators. A formula of generators is found for the solution semigroups of evolution equations with infinite delay on the general phase space. It is applied to the study of the spectrum, eigenfunctions of the semigroup, as well as to the study of stability.2. The flow satisfying Kutta condition can be computed numerically as precisely as possible through a finite element computation of stream function of the velocity field using the transpearent non local boundary conditions imposed on artificial boundaries suitably introduced.3. The vibration and wave propagation phenomena are studied for the following themes : Proposal of perturbation method for structural-acoustic coupled vibration problem and its justification : Proposal of the iteration method for the Helmholtz equation based on the domain decomposition technique and proof of its efficiency : Consideration of the relation between inf-sup condition and spectral pollution. The equation is derived for the vibration of a elastic string in. 3-dimensional, and its certain justification is shown.4. A convergent finite element scheme for advection equations of convection equations or convection equations is proposed. The error order estimates which is best possible is proved. The scheme is successfully applied to an advection equation for the densities in the density dependent Stokes equations.5. Existence and regularity for a solution of the evolution problem associated to p-harmonic maps is established if the target manifold has a non-positive sectional curvature.