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Preconditioning operators and $L^\infty$ attractor for a class of reaction-diffusion systems
We suggest an approach for proving global existence of bounded solutions and existence of a maximal attractor in$L^\infty$ for a class of abstract $3\times 3$ reaction-diffusion systems. The motivation comes from theconcrete example of ``facilitated diffusion'' system with different non-homogeneous boundary conditionsmodelling the blood oxigenation reaction $Hb+O_2 \rightleftharpoons HbO_2$.The method …