Boundary Blow-up Solutions of Second Order Quasilinear Equation on Infinite Cylinders

TL;DR

This paper investigates the existence and properties of large solutions to p-Laplacian type equations on infinite cylindrical domains, establishing convergence from finite to infinite cylinders and extending results to more general operators.

Contribution

It introduces a method to analyze large solutions on infinite cylinders and generalizes the results to operators with gradient non-linearity.

Findings

Large solutions on finite cylinders converge to solutions on infinite cylinders.

Any such solution matches the large solution on each cross-section.

Results are extended to operators with non-linear gradient dependence.

Abstract

This article studies large solutions, for a class of quasi-linear equations involving p-Laplacian on the infinite cylindrical domains. We study the wellposedness of weak large solutions on infinite cylinders by the convergence of large solutions on finite cylinders and observe that any such solution coincides with the large solution on its cross-section. Finally, the results are generalized to a class of operators involving non-linearity in the gradient.