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• W2159462294 abstract "A new linearization method is introduced for smooth short-time solvability of initial boundary value problems for nonlinear evolution equa- tions. The technique based on an inverse function theorem of Nash-Moser type is illustrated by an application in the parabolic case. The equation and the boundary conditions may depend fully nonlinearly on time and space vari- ables. 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 regular- ity in analytic semigroup theory, higher order elliptic a priori estimates and simultaneous continuity in trace theorems in Sobolev spaces. The purpose of this paper is to introduce a new linearization method for smooth short-time solvability of initial boundary value problems for nonlinear evolution equations. The technique based on an inverse function theorem of Nash-Moser 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 general Theorem 4.3 applies to a nonlinear evolutionary boundary value problem provided that the linearized equation with linearized boundary conditions is well posed; here a loss of derivatives is allowed in the estimates of the linearized problem. An application in the parabolic case is given in Theorem 8.1. We mention some points of the proof which might be of independent interest. A Borel's theorem is applied to transform the compatibility conditions. A trace the- orem is proved for normal boundary operators in spaces of smooth functions using tame splitting theory in Frechet spaces. Some results on simultaneous continuity in trace theorems in Sobolev spaces are proved. In the application, higher order Sobolev norm estimates including the dependence of the constants from the coef- ficients are derived for the linearized parabolic problem using analytic semigroup theory involving evolution operators and maximal regularity. Inverse function theorems of Nash-Moser type (13, 15, 25, 34, 39) have been applied to partial dierential equations in several papers, for instance, concerning" @default.
• W2159462294 created "2016-06-24" @default.
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• W2159462294 date "2003-01-01" @default.
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• W2159462294 title "Nash-Moser techniques for nonlinear boundary-value problems." @default.
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