| Abstract: |
| The global-in-time existence of weak and renormalized solutions
toreaction-cross-diffusion systems for an arbitrary number of
variables inbounded domains with no-flux boundary conditions are
proved. Thecross-diffusion part describes the segregation of
population species and is ageneralization of the SKT model. The
diffusion matrix is not diagonal andgenerally neither symmetric nor
positive semi-definite, but the systempossesses a formal
gradient-flow or entropy structure. The reaction part is
ofLotka-Volterra type for weak solutions or includes reversible
reactions ofmass-action kinetics and does not obey any growth
condition for renormalizedsolutions. Furthermore, we prove the
uniqueness of bounded weak solutions to a specialclass of
cross-diffusion systems, and the weak-strong uniqueness
ofrenormalized solutions to the general reaction-cross-diffusion
cases. |
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