Approximation properties of the q-sine bases

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Abstract

For q >= 12/11, the eigenfunctions of the nonlinear eigenvalue problem associated with the one-dimensional q-Laplacian are known to form a Riesz basis of L-2(0, 1). We examine in this paper the approximation properties of this family of functions and its dual, and establish a non-orthogonal spectral method for the p-poisson boundary value problem and its corresponding parabolic time-evolution initial value problem with stochastic forcing. The principal objective of our analysis is the determination of optimal values of q for which the best approximation is achieved for a given p problem.

Original languageEnglish
Pages (from-to)2690-2711
Number of pages22
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume467
Issue number2133
DOIs
Publication statusPublished - 8 Sep 2011

Keywords

  • p-Laplace Cauchy problem
  • p-Laplace evolution problem with stochastic forcing
  • q-sine basis
  • non-orthogonal spectral method
  • FINITE-ELEMENT APPROXIMATION
  • P-LAPLACIAN
  • FAST/SLOW DIFFUSION
  • GROWING SANDPILES
  • EQUATION
  • REGULARITY
  • LIMIT
  • MODEL

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