Oberwolfach Tagungsbericht 26/1999 Partial Di erential Equations 13.06.1999 { 19.06.1999 This meeting was organized by L. C. Evans (Berkeley), S. M uller (MPI Leipzig) and E. Kuwert (Freiburg). The 22 delivered talks addressed a broad spectrum of questions for nonlinear partial di erential equations. Most of the considered problems arise in geometry or in physics, as for example submanifolds w...

Symbolic Reachability Computation for Families of Linear Vector Fields Gerardo Lafferriere Department of Mathematical Sciences Portland State University, P.O. Box 751, Portland, OR 97207-0751. [email protected] George J. Pappas Department of Electrical Engineering University of Pennsylvania, 200 South 33rd Street, Philadelphia, PA 19104. [email protected] Sergio Yovine VERIMAG Centre Equat...

Solvability of forward–backward stochastic di erential equations with nonsmooth coe cients is considered using the Four-Step Scheme and some approximation arguments. For the onedimensional case, the existence of an adapted solution is established for the equation which allows the di usion in the forward equation to be degenerate. As a byproduct, we obtain the existence of a viscosity solution t...

We consider a system of ordinary di erential equations consisting of a singularly perturbed scalar di erential equation of second order and a scalar di erential equation of rst or second order and study a Neuman-Cauchy or a Neuman-Dirichlet problem. We assume that the degenerate equation has two intersecting solutions such that the standard theory for systems of Tichonov's type cannot be applie...

This paper surveys recent results on the classi cation of di erential invari ants of transformation groups and their applications to invariant di erential equations and variational problems Consider a group of transformations acting on a jet space coordinatized by the inde pendent variables the dependent variables and their derivatives Scalar functions which are not a ected by the group transfo...

Some oscillation criteria for the oscillatory behavior of fourth order superlinear dynamic equations on time scales are established. Criteria are proved that ensure that all solutions of superlinear and linear equations are oscillatory. Many of our results are new for corresponding fourth order superlinear di¤erential equations and fourth order superlinear di¤erence equations.

Continuous system dynamics can be described by possibly large systems of di erential equations These can be either ordinary di erential equations ODEs or contain algebraic constraints as well to form di erential and algebraic equations DAEs Complex systems such as aircraft often operate in di erent modes of continuous operation and when mode changes occur the continuous dynamics change abruptly...

In this paper, we study the existence and stability of traveling waves in lattice dynamical systems, in particular, in lattice ordinary di erential equations (lattice ODE's) and in coupled map lattices (CML's). Instead of employing the moving coordinate approach as for partial di erential equations, we construct a local coordinate system around a traveling wave solution of a lattice ODE, analog...

Game theory is concerned with optimization problems involving several players with conicting interests. Di erential games are an interesting area inside this eld in which the problem is formulated by means of dynamical systems. In spite that the theoretical solution of di erential games is well known, faced with large-scale, complex systems, analytical or, even, numerical methods are not usuall...

The problem of simultaneous reduction of real matrices by either orthogo nal similarity or orthogonal equivalence transformations is considered Based on the Jacobi idea of minimizing the sum of squares of the complementary part of the desired form to which matrices are reduced the projected gradi ent method is used in this paper It is shown that the projected gradient of the objective function ...