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...

This paper summarizes recent results on the number and characterization of di erential invariants of transformation groups Generalizations of theorems due to Ovsiannikov and to M Green are presented as well as a new approach to nding bounds on the number of independent di erential invariants Consider a group of transformations acting on a jet space coordinatized by the inde pendent variables th...

In this paper, we study general linear systems of delay di erential-algebraic equations (DDAEs) of arbitrary order. We show that under some consistency conditions, every linear high-order DAE can be reformulated as an underlying high-order ordinary di erential equation (ODE) and that every linear DDAE with single delay can be reformulated as a high-order delay di erential equation (DDE). We der...

In this paper we study polynomial maps of vector spaces zi → Ai1i2···is i zi1zi2zi3 · · · zis and their eigenvectors and eigenvalues. The new quantity called complanart is de ned. Complanarts determine complanarity of solution vectors of systems of polynomial equations. Evaluation of complanart is reduced to evaluation of resultants. As in linear case, the pattern of eigenvectors de nes the pha...

This note gives a theory of state transition matrices for linear systems of fuzzy di#erential equations. This is used to give a fuzzy version of the classical variation of constants formula. A simple example of a time-independent control system is used to illustrate the methods. While similar problems to the crisp case arise for time-dependent systems, in time-independent cases the calculations...

We study a new class of backward stochastic di€erential equations, which involves the integral with respect to a continuous increasing process. This allows us to give a probabilistic formula for solutions of semilinear partial di€erential equations with Neumann boundary condition, where the boundary condition itself is nonlinear. We consider both parabolic and elliptic equations.

in this paper, a new and ecient approach is applied for numerical approximationof the linear dierential equations with variable coecients based on operational matriceswith respect to hermite polynomials. explicit formulae which express the hermite expansioncoecients for the moments of derivatives of any dierentiable function in terms of theoriginal expansion coecients of the function itse...

This work presents the arguments for the possibility of approximating some discontinuous dynamical systems with continuous or even smooth dynamical systems. The discontinuous di€erential equation, which describes the system, is transformed into a di€erential inclusion and then into a di€erential equation with continuous or smooth right-hand side. As an example a generalization of the equations ...

Di€usion and convection coecients of the aerated ̄ow in a hydraulic jump are estimated in the framework of an optimal control problem. The speci®c gravity of air±water mixture is governed by a steady state convection di€usion partial di€erential equation. The governing equation includes the di€usion coecient and the convection coecient, which are taken as the control variables to minimize a ...

In a series of papers, starting with [Fully nonlinear stochastic partial di¤erential equations. C. R. Acad. Sci. Paris Sér. I Math. 326 (1998), no. 9] Lions and Souganidis proposed a (pathwise) theory for fully non-linear stochastic partial di¤erential equations. We present here a (partial) extension towards certain spatial dependence in the noise term. The main novelty is the use of rough path...