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The goal of this work is to establish the global existence of nonnegativeclassical solutions in all dimensions for a system of highly nonlinearreaction-diffusion equations. We address the case for different diffusioncoefficients and the system of reversible reactions with non-homogeneousNeumann boundary conditions. The systems are assumed to satisfy only the masscontrol condition and to have locally Lipschitz nonlinearities with arbitrarygrowth. The key aspect of this work is that we didn't assume that the diffusioncoefficients are close to each other. We utilize the duality method and theregularization of the heat operator to derive the result. We also illustratethe global in time bounds for the solutions. The application includes concretecorrosion in sewer pipes or sulfate corrosion in sewer pipes.

Global existence and uniform boundedness of the classical solutions for the system of multi-species transport with mass control