## Approximation of Nonlinear Evolution SystemsApproximation of Nonlinear Evolution Systems |

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analysis applied approximation assumed Banach space boundary bounded Brézis Cauchy problem Chapter compact condition continuous function continuously embedded convergence convex Corollary defined denote derivative domain elliptic equivalent estimate evolution operators existence finite finite-dimensional fluid follows given H(uo H(uš hence Hilbert space Hölder's inequality holds inequality initial datum integration isomorphism Lebesgue integrable Lemma Lipschitz continuous lower semicontinuity mapping Math maximal monotone method models N-width Navier–Stokes nonlinear nonnegative normed linear space Note obtain partial differential equations partitions pointwise polynomial porous-medium equation Proof Proposition pseudomonotone quasi-stability regularity relation result satisfying Section self-adjoint semidiscrete semigroup sequence smoothing ſº Sobolev Sobolev spaces stability Stefan problem subset subspace Suppose tensor term Theorem theory two-phase Stefan problem unique variables weak solution weakly