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In this paper we consider a semilinear parabolic equation in an infinitecylinder. The spatially varying nonlinearity is such that it connects two(spatially independent) bistable nonlinearities in a compact set in space. Weprove that, given such a setting, a traveling wave obeying the equation withthe one bistable nonlinearity and starting at the respective side of thecylinder, will converge to a traveling wave solution prescribed by thenonlinearity on the other side.

A heteroclinic orbit connecting traveling waves pertaining to different nonlinearities