Nonnegative solutions to the reaction-diffusion equations for prey-predator models with the dormancy of predators
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A Priori
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The time-global unique solvability on the reaction–diffusion equations for preypredator models and dormancy on predators is established. The crucial step is to construct time-local nonnegative classical solutions by using a new approximation associated with time-evolution operators. Although the system does not equip usual comparison principles, a priori bounds are derived, so solutions are extended time-globally. Via observations to the corresponding ordinary differential equations, invariant regions and asymptotic behaviors of solutions are also investigated.
2017 ◽
Vol 263
(11)
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pp. 7601-7626
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2016 ◽
Vol 41
(5)
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pp. 785-811
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2015 ◽
Vol 25
(05)
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pp. 1550063
2014 ◽
Vol 52
(7)
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pp. 1984-2012
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2019 ◽
Vol 45
(6)
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pp. 483-524
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