Resonance for Singular Perturbation Problems

Consider the resonance for a second-order equation εy"-xpy’+ qy = 0. Another proof is given for the necessity of the Matkowsky condition and the connection with a regular eigenvalue problem is established. Also, if p, q are analytic, necessary and sufficient conditions are derived

Numerical Methods for Singular Perturbation Problems

Consider the two-point boundary value problem for a stiff system of ordinary differential equations. An adaptive method to solve these problems even when turning points are present is discussed

Ein weiterer Fundort von Cicindela germanica L. 1758 (Coleoptera: Cicindelidae) aus Ostwestfalen

Autoren älterer Arbeiten melden die Art des öfteren als zahlreich, sehr häufig oder auch massenhaft auftretend (WESTHOFF 1881 , VERHOEFF 1890, ROETTGEN 1911, HORION 1941 u.a.). Gleichzeitig wird aber auch betont, daß so häufiges Auftreten lokal beschränkt ist und die Art auch in weiten Gebieten fehlt. In jüngeren Arbeiten wird von einem Rückgang oder gar vom Aussterben in den ehemaligen Vorkommensgebieten berichtet (BARNER 1937, HORION 1941). Wegen der Seltenheit der Nachweise in der zweiten Hälfte dieses Jahrhunderts und des allgemeinen Rückgangs der Art, soll hier ein jüngerer Nachweis bekannt gemacht werden: Am 7.6.1981 sah ich ein Exemplar im Naturschutzgebiet "Stockberg" bei Höxter-Ottbergen

Stability of quasi-linear hyperbolic dissipative systems

In this work we want to explore the relationship between certain eigenvalue condition for the symbols of first order partial differential operators describing evolution processes and the linear and nonlinear stability of their stationary solutions.Comment: 16 pages, Te

A priori estimates in terms of the maximum norm for the solutions of the Navier–Stokes equations

AbstractIn this paper, we consider the Cauchy problem for the incompressible Navier–Stokes equations with bounded initial data and derive a priori estimates of the maximum norm of all derivatives of the solution in terms of the maximum norm of the initial velocity field. For illustrative purposes, we first derive corresponding a priori estimates for certain parabolic systems. Because of the pressure term, the case of the Navier–Stokes equations is more difficult, however

Global existence and exponential decay for hyperbolic dissipative relativistic fluid theories

We consider dissipative relativistic fluid theories on a fixed flat, compact, globally hyperbolic, Lorentzian manifold. We prove that for all initial data in a small enough neighborhood of the equilibrium states (in an appropriate Sobolev norm), the solutions evolve smoothly in time forever and decay exponentially to some, in general undetermined, equilibrium state. To prove this, three conditions are imposed on these theories. The first condition requires the system of equations to be symmetric hyperbolic, a fundamental requisite to have a well posed and physically consistent initial value formulation. The second condition is a generic consequence of the entropy law, and is imposed on the non principal part of the equations. The third condition is imposed on the principal part of the equations and it implies that the dissipation affects all the fields of the theory. With these requirements we prove that all the eigenvalues of the symbol associated to the system of equations of the fluid theory have strictly negative real parts, which in fact, is an alternative characterization for the theory to be totally dissipative. Once this result has been obtained, a straight forward application of a general stability theorem due to Kreiss, Ortiz, and Reula, implies the results above mentioned.Comment: 10 pages, Late

On the well posedness of Robinson Trautman Maxwell solutions

We show that the so called Robinson-Trautman-Maxwell equations do not constitute a well posed initial value problem. That is, the dependence of the solution on the initial data is not continuous in any norm built out from the initial data and a finite number of its derivatives. Thus, they can not be used to solve for solutions outside the analytic domain.Comment: 9 page