Wazewski's Method for Nonlinear Evolution Equations

S. G. Lobanov

State University – Higher School of Economics

Abstract: We justify a method for reducing a wide class of nonlinear equations (including several partial differential equations) to ordinary differential equations in locally convex spaces. The possibilities of this method are demonstrated by an example of a class of nonlinear hyperbolic partial differential equations.

Keywords: evolution equation, hyperbolic partial differential equation, ordinary differential equation, locally convex space, mapping, fixed point, Hadamard differentiability.

UDC: 517.911:517.956.3

Received: 20.06.2006

DOI: 10.4213/mzm4717

 English version: Mathematical Notes, 2008, 83:5, 643–651

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