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Talk

Linear PDE with Constant Coefficients

  • Marc Härkönen (Georgia Institute of Technology, Atlanta)
E1 05 (Leibniz-Saal)

Abstract

In an undergraduate differential equations course we learn to solve a homogeneous linear ordinary differential equation with constant coefficients by finding roots of the characteristic polynomial. Thus the problem of solving an ODE is reduced to factoring a univariate polynomial. A generalization of this was found in the 1960s for systems of linear PDE. The Fundamental Theorem by Ehrenpreis and Palamodov asserts that solutions to a PDE system can be represented by a finite sum of integrals over some algebraic variety. This representation can be used describe a primary decomposition of an ideal or module. This talk presents the main historical results, along with recent algorithms.

Mirke Olschewski

MPI for Mathematics in the Sciences Contact via Mail

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