We give a complete characterization of the boundary traces ‘i (i D 1;:::; K) supporting spiraling waves, rotating with a given angular speed !, which appear as singular limits of competition-diffusion systems of the type (Formula presented) as β ! C1. Here Ω is a rotationally invariant planar set, and aij > 0 for every i and j. We tackle also the homogeneous Dirichlet and Neumann boundary conditions, as well as entire solutions in the plane. As a byproduct of our analysis, we detect explicit families of eternal, entire solutions of the pure heat equation, parametrized by ! 2 R, which reduce to homogeneous harmonic polynomials for ! D 0.
Rotating spirals in segregated reaction-diffusion systems
Verzini, Gianmaria;
2025-01-01
Abstract
We give a complete characterization of the boundary traces ‘i (i D 1;:::; K) supporting spiraling waves, rotating with a given angular speed !, which appear as singular limits of competition-diffusion systems of the type (Formula presented) as β ! C1. Here Ω is a rotationally invariant planar set, and aij > 0 for every i and j. We tackle also the homogeneous Dirichlet and Neumann boundary conditions, as well as entire solutions in the plane. As a byproduct of our analysis, we detect explicit families of eternal, entire solutions of the pure heat equation, parametrized by ! 2 R, which reduce to homogeneous harmonic polynomials for ! D 0.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
