| Abstract: |
| In this talk I discuss some recent advances on global existence of reaction-diffusion systems, where only natural assumptions such as quasi-positivity and mass controlled are imposed. It is shown that, in the case of smooth diffusion, the system with quadratic growing nonlinearities has a unique global classical solution, which is also bounded uniformly in time provided that the mass is dissipated. For non-smooth diffusion coefficients, the global existence of bounded weak solutions is shown by a generalised $L^p$-energy method and intermediate sum condition with sub-critical growth of nonlinearities. |
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