Monotone heteroclinic solutions to semilinear PDEs in cylinders and applications

2024/07/05 by De Regibus, Fabio, Ruiz, David · 2 citations
#35B08 #35J25 #35Q35 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2407.04546

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.

Cited by

• Least total curvature solutions to steady Euler system and monotone solutions to semilinear equations in a strip
• Rigidity results for finite energy solutions to the stationary 2D Euler equations

Related

• Least total curvature solutions to steady Euler system and monotone solutions to semilinear equations in a strip
• Semilinear equations in bounded cylinders: Morse index and bifurcation from one-dimensional solutions
• Existence of heteroclinic solution for a double well potential equation\n in an infinite cylinder of \ℝ^N
• Symmetry and monotonicity results for solutions of semilinear PDEs in sector-like domains
• Center manifolds without a phase space for quasilinear problems in elasticity, biology, and hydrodynamics