Preservation of spatial patterns by a hyperbolic equation
Anatoli V. Babin · Discrete and Continuous Dynamical Systems · 2004
Oscillations in a nonlinear, strongly spatially inhomogenious media are described by scalar semilinear hyperbolic equations with coefficients strongly depending on spatial variables. The spatial patterns of solutions may be very complex, we describe them in terms of binary lattice functions and show that the patterns are preserved by the dynamics. We prove that even when solutions of the equations are not unique, the large-scale spatial patterns of solutions are preserved. We consider arbitrary large spatial domains and show that the number of distinct invariant domains in the function space depends exponentially on the volume of the domain.