Annals of Mathematical Sciences and Applications

Volume 9 (2024)

Number 2

Weighted $p$-Laplacian parabolic equation and $(p, \alpha, \beta)$-spectrum

Pages: 405 – 437

DOI: https://dx.doi.org/10.4310/AMSA.2024.v9.n2.a5

Authors

Zhen Shuang (Department of Mathematics and Statistics, Memorial University, St. John’s, Newfoundland, Canada)

Jie Xiao (Department of Mathematics and Statistics, Memorial University, St. John’s, Newfoundland, Canada)

Abstract

A weighted $p$-Laplacian parabolic equation is studied and applied to achieve $(p, \alpha, \beta)$-spectrum and decomposition of a signal. Weak solutions to the equation are existent by the Faedo–Galerkin method. $(p, \alpha, \beta)$-spectrum and decomposition are acquired by means of eigenfunctions of $\Delta_{p,\alpha}$ and fractional order derivatives.

Keywords

weighted $p$-Laplace, $(p, \alpha, \beta)$-spectrum, signal decomposition

2010 Mathematics Subject Classification

Primary 35Axx, 35K55, 68U10. Secondary 35B05.

Received 21 July 2023

Accepted 19 August 2023

Published 15 August 2024