Global existence for a class of quadratic reaction–diffusion systems with nonlinear diffusions and L1 initial data. (June 2016) - Pierre, Michel; Rolland, Guillaume
Abstract: In this work, existence of global weak solutions in any space dimension is proven for a class of reaction–diffusion systems with L 1 -initial data, nonlinear diffusions and at most quadratic reactions. The proof relies on a dimension-independent L 2 -estimate, based on a total mass control assumption. If initial data are in L 2, this estimate provides a control of the quadratic nonlinearities in L 1 up to t = 0 . In the case of L 1 -initial data, we prove that the L 2 -estimate can be localized in time, which allows to pass to the limit in an approximate system for t > 0 . We then prove the continuity of the solution in L 1 at t = 0 .