Nash–Moser iteration and singular perturbations
نویسنده
چکیده
We present a simple and easy-to-use Nash–Moser iteration theorem tailored for singular perturbation problems admitting a formal asymptotic expansion or other family of approximate solutions depending on a parameter ε → 0. The novel feature is to allow loss of powers of ε as well as the usual loss of derivatives in the solution operator for the associated linearized problem. We indicate the utility of this theorem by describing sample applications to (i) large-amplitude, high-frequency WKB solutions of quasilinear hyperbolic systems, and (ii) existence of small-amplitude profiles of quasilinear relaxation systems.
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