Work

Monotone heteroclinic solutions to semilinear PDEs in cylinders and applications

Year: 2025

Type: article

Abstract: In this paper we show the existence of strictly monotone heteroclinic type solutions of semilinear elliptic equations in cylinders. The motivation of this construction is twofold: first, it implies the existence of an entire bounded solution of a semilinear equation without critical points which is not one-dimensional. Second, this gives an example of a bounded stationary solution for the 2D Euler equations without stagnation points which is not a shear flow, completing previous results of Hamel and Nadirashvili. The proof uses a minimization technique together with a truncation argument, and a limit procedure.

Source: Calculus of Variations and Partial Differential Equations

DOI: 10.1007/s00526-025-02975-x

Authors: Fabio De Regibus, David Ruiz

Institution: Universidad de Granada

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: European Commission, Ministerio de Ciencia e Innovación, Universidad de Granada, Agencia Estatal de Investigación