Existence results for nonlinear Fourier problems with variable exponent growth
Abstract
We study nonlinear problems which use the generalized $\alpha(x)-$Laplacian operator under Fourier boundary conditions with $L^{1}$ data. Our research establishes both weak and entropy solutions through the framework of variable exponent Sobolev spaces. Our solution method uses monotone operator theory and appropriate approximation methods to develop a unified approach for dealing with nonlinearities that exhibit variable growth. These findings help expand knowledge about nonlinear Fourier-type problems while demonstrating how entropy formulations enable well-posedness for problems with minimal data requirements.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Navier-Stokes equation solutions
Numerical methods in inverse problems
Publication details
- Journal / source
- Mathematical Modelling and Analysis
- Publisher
- Vilnius Gediminas Technical University
- Volume
- 31
- Issue
- 3
- Pages
- 452–475
- Publication date
- 18 June 2026
- Language
- EN