The nonlinear steepest descent method: Asymptotics for initial-boundary\n value problems

2015/02/01 by Jonatan Lenells, Lenells, Jonatan
Engineering · Mathematics · #35Q15 #35Q53 #41A60 #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1502.00217

openalex publication_date 2015/02/01 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

We consider the rigorous derivation of asymptotic formulas for\ninitial-boundary value problems using the nonlinear steepest descent method. We\ngive detailed derivations of the asymptotics in the similarity and self-similar\nsectors for the mKdV equation in the quarter plane. Precise and uniform error\nestimates are presented in detail.\n

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