Preservation of spatial patterns by a hyperbolic equation. (Q1433902)

The author considers scalar semilinear hyperbolic equations with coefficients explicitly depending on spatial variables. Here the author deals with arbitrary large spatial domains, the conditions which he imposes on the equations do not depend on the size of the domain. The author proves that even when the solutions of the equations are not unique the spatial patterns of solutions are preserved. The result of the author implies the existence of extremely many invariant domains of the dynamics generated by a hyperbolic partial differential equation even when the dynamics may be multivalued.