| Tartalmi leírás: |
One of the classical maximum principles state that any nonnegative solution of a
proper elliptic PDE attains its maximum on the boundary of a bounded domain. We
suitably extend this principle to nonlinear cooperative elliptic systems with diagonally
dominant coupling and with mixed boundary conditions. One of the consequences
is a preservation of nonpositivity, i.e. if the coordinate functions or their
uxes are
nonpositive on the Dirichlet or Neumann boundaries, respectively, then they are
all nonpositive on the whole domain as well. Such a result essentially expresses
that the studied PDE system is a qualitatively reliable model of the underlying real
phenomena, such as proper reaction-diffusion systems in chemistry.
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