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Nonlinear Stability of Periodic Roll Solutions in the Real Ginzburg–Landau Equation Against $$C_{\textrm{ub}}^m$$-Perturbations
The real Ginzburg-Landau equation arises as a universal amplitude equation for the description of pattern-forming systems exhibiting a Turing bifurcation. It possesses spatially periodic roll solutions which are known to be stable against localized perturbations. It is the purpose of this paper to prove their stability against bounded perturbations, which …