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A dynamical approach to semilinear elliptic equations
- Publication Year :
- 2019
-
Abstract
- A characterization of a semilinear elliptic partial differential equation (PDE) on a bounded domain in $\mathbb{R}^n$ is given in terms of an infinite-dimensional dynamical system. The dynamical system is on the space of boundary data for the PDE. This is a novel approach to elliptic problems that enables the use of dynamical systems tools in studying the corresponding PDE. The dynamical system is ill-posed, meaning solutions do not exist forwards or backwards in time for generic initial data. We offer a framework in which this ill-posed system can be analyzed. This can be viewed as generalizing the theory of spatial dynamics, which applies to the case of an infinite cylindrical domain.<br />Comment: v2: minor corrections and notational changes
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1907.09986
- Document Type :
- Working Paper