  The time-global unique solvability on the reaction diffusion equations for
prey-predator models with density-dependent inhibitor and dormancy on predators
is established. The crucial step of the proof is to construct time-local
non-negative classical solutions. To do so, new successive approximation and
theories of time-evolution operators are used. Due to the maximum principle,
the solutions are extended time-globally. Via analysis on the corresponding
ordinary differential equations, invariant regions and asymptotic behaviors of
solutions are also investigated.
