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

TL;DR

This paper proves the global existence and boundedness of classical solutions for multi-species reaction-diffusion systems with mass control, even with differing diffusion coefficients and complex boundary conditions.

Contribution

It establishes the first global existence results for such systems without assuming similar diffusion coefficients, using duality and heat operator regularization techniques.

Findings

Solutions are globally bounded in time.

Applicable to corrosion processes in sewer pipes.

Works for systems with arbitrary nonlinear growth.

Abstract

The goal of this work is to establish the global existence of nonnegative classical solutions in all dimensions for a system of highly nonlinear reaction-diffusion equations. We address the case for different diffusion coefficients and the system of reversible reactions with non-homogeneous Neumann boundary conditions. The systems are assumed to satisfy only the mass control condition and to have locally Lipschitz nonlinearities with arbitrary growth. The key aspect of this work is that we didn't assume that the diffusion coefficients are close to each other. We utilize the duality method and the regularization of the heat operator to derive the result. We also illustrate the global in time bounds for the solutions. The application includes concrete corrosion in sewer pipes or sulfate corrosion in sewer pipes.