Die Lösung der partiellen Differentialgleichung mit gewissen Nebenbedingungen
Difference methods for the Darboux problem for functional partial differential equations
Difference Schemes with Best Possible Truncation Error.
Differential operators with non dense domain
Differenzenverfahren zur Berechnung periodischer Lösungen von hyperbolischen Differentialgleichungen.
Diffraction des singularités analytiques dans les problèmes aux limites de la physique mathématique par les méthodes de Kawai-Kashiwara et Sjöstrand
Diffractive nonlinear geometric optics
Diffusion phenomenon for second order linear evolution equations
We present an abstract theory of the diffusion phenomenon for second order linear evolution equations in a Hilbert space. To derive the diffusion phenomenon, a new device developed in Ikehata-Matsuyama [5] is applied. Several applications to damped linear wave equations in unbounded domains are also given.
Dirac fields on asymptotically flat space-times [Book]
Direct approach to mean-curvature flow with topological changes
This contribution deals with the numerical simulation of dislocation dynamics. Dislocations are described by means of the evolution of a family of closed or open smooth curves , . The curves are driven by the normal velocity which is the function of curvature and the position. The evolution law reads as: . The motion law is treated using direct approach numerically solved by two schemes, i. e., backward Euler semi-implicit and semi-discrete method of lines. Numerical stability is improved...
Dirichlet and Neumann problems for string equation, Poncelet problem and Pell-Abel equation.
Dirichlet problem for a nonlinear conservation law.
In this paper we propose the study of a first-order non-linear hyperbolic equation in a bounded domain. We give a result of existence and uniqueness of the entropic measure-valued solution and of the entropic weak solution; for some general assumptions on the data.
Discontinous Solutions of a Nonlinear Hyperbolic Equation with Unilateral Constraints.
Discontinuous Galerkin method with Godunov-like numerical fluxes for traffic flows on networks. Part II: Maximum principle
We prove the maximum principle for a discontinuous Galerkin (DG) method applied to the numerical solution of traffic flow problems on networks described by the Lighthill-Whitham-Richards equations. The paper is a followup of the preceding paper, Part I, where stability of the scheme is analyzed. At traffic junctions, we consider numerical fluxes based on Godunov’s flux derived in our previous work. We also construct a new Godunov-like numerical flux taking into account right of way at the junction...
Discontinuous Galerkin method with Godunov-like numerical fluxes for traffic flows on networks. Part I: stability
We study the stability of a discontinuous Galerkin (DG) method applied to the numerical solution of traffic flow problems on networks. We discretize the Lighthill-Whitham-Richards equations on each road by DG. At traffic junctions, we consider two types of numerical fluxes that are based on Godunov’s numerical flux derived in a previous work of ours. These fluxes are easily constructible for any number of incoming and outgoing roads, respecting the drivers’ preferences. The analysis is split into...
Discontinuous solutions of the Cauchy problems for a scalar equation in nonconservative form
Discontinuous travelling wave solutions for a class of dissipative hyperbolic models
Discontinuous shock structure solutions for a general system of balance laws is considered in order to investigate the problem of connecting two equilibrium states lying on different sides of a singular barrier representing a locus of irregular singular points for travelling waves. Within such a theoretical setting a governing system of monoatomic gas is considered.
Discontinuous wave equations and a topological degree for some classes of multi-valued mappings
The Leray-Schauder degree is extended to certain multi-valued mappings on separable Hilbert spaces with applications to the existence of weak periodic solutions of discontinuous semilinear wave equations with fixed ends.
Dispersive and Strichartz estimates for the wave equation in domains with boundary
In this note we consider a strictly convex domain of dimension with smooth boundary and we describe the dispersive and Strichartz estimates for the wave equation with the Dirichlet boundary condition. We obtain counterexamples to the optimal Strichartz estimates of the flat case; we also discuss the some results concerning the dispersive estimates.
Dispersive estimates for a linear wave equation with electromagnetic potential.