The Existence of Wave Operators in Scattering Theory.
The exponential stability of a coupled hyperbolic/parabolic system arising in structural acoustics.
The extended tanh method and the exp-function method to solve a kind of nonlinear heat equation.
The extended tanh-mehtod for finding traveling wave solutions of nonlinear evolution equations.
The exterior Dirichlet problem for quasi linear elliptic equations with small boundary data.
The far-field modelling of transonic compressible flows
We present a method for the construction of artificial far-field boundary conditions for two- and three-dimensional exterior compressible viscous flows in aerodynamics. Since at some distance to the surrounded body (e.g. aeroplane, wing section, etc.) the convective forces are strongly dominant over the viscous ones, the viscosity effects are neglected there and the flow is assumed to be inviscid. Accordingly, we consider two different model zones leading to a decomposition of the original flow...
The Fast Fourier Transform and the Numerical Solution of One-Dimensional Boundary Integral Equations.
The FBI transform, operators with nonsmooth coefficients and the nonlinear wave equation
The aim of this work is threefold. First we set up a calculus for partial differential operators with nonsmooth coefficients which is based on the FBI (Fourier-Bros-Iagolnitzer) transform. Then, using this calculus, we prove a weaker version of the Strichartz estimates for second order hyperbolic equations with nonsmooth coefficients. Finally, we apply these new Strichartz estimates to second order nonlinear hyperbolic equations and improve the local theory, i.e. prove local well-posedness for initial...
The Fermi surface for the discretized Maxwell equations
The Feynman path integral as an improper integral over the Sobolev space
The Feynman-Kac formula for a system of parabolic equations
The fictitious domain method for the mixed finite element approximation of the wave equation
The fifth-order Korteweg-de Vries equation.
The finite element method for nonlinear elliptic equations with discontinuous coefficients.
The Finite Element Method for Parabolic Equations. I. A Posteriori Error Estimation
The Finite Element Method for Parabolic Equations. II. A Posteriori Error Estimation and Adaptive Approach
The Finite Element Method with Lagrangian Multipliers.
The finite element method with nodes moving along the characteristics for convection-diffusion equations.
The Finite Element Method with Non-Uniform Mesh Sizes Applied to the Exterior Helmholtz Problem.
The finite element solution of elliptic and parabolic equations using simplicial isoparametric elements