Electron. J. Diff. Eqns., Vol. 2003(2003), No. 54, pp. 133.
NashMoser techniques for nonlinear boundaryvalue problems
Markus Poppenberg
Abstract:
A new linearization method is introduced for smooth
shorttime solvability of initial boundary value problems for
nonlinear evolution equations. The technique based on an inverse
function theorem of NashMoser type is illustrated by an
application in the parabolic case. The equation and the boundary
conditions may depend fully nonlinearly on time and space
variables. The necessary compatibility conditions are transformed
using a Borel's theorem. A general trace theorem for normal
boundary conditions is proved in spaces of smooth functions by
applying tame splitting theory in Frechet spaces. The
linearized parabolic problem is treated using maximal regularity
in analytic semigroup theory, higher order elliptic a priori
estimates and simultaneous continuity in trace theorems in Sobolev
spaces.
Submitted July 14, 2002. Published May 5, 2003.
Math Subject Classifications: 35K60, 58C15, 35K30.
Key Words: NashMoser, inverse function theorem,
boundaryvalue problem, parabolic, analytic semigroup,
evolution system, maximal regularity, trace theorem.
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Markus Poppenberg
Fachbereich Mathematik
Universitat Dortmund
D44221 Dortmund, Germany
email: poppenberg@math.unidortmund.de 
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