Abstract
The model we study deals with a population of marine invertebrates structured by size whose life stage is composed of adults and pelagic larvae such as barnacles contained in a local habitat. We prove existence and uniqueness of a continuous positive global mild solution and we give an estimate of it. We prove also that this solution is the strong solution of the problem.
Highlights
A famous American zoologist of Swiss origin, Louis Agassiz, lived in the XIX century defined the barnacles like “little shrimps hanging from the rock with their heads, locked in a limestone house and kicked throwing food into their mouths”.They belong to a species of crustaceans, marine invertebrates whose life is composed of two stages, pelagic larvae and adult sessile.Barnacles have two larval stages: the first spends its time as part of zooplankton floating wherever the wind, waves, currents, and tides may take it
We prove the existence of a mild solution global in time, by using affine semigroup techniques
We get estimates of the solution to prove that the local solution is global in time, and eventually, we prove that this solution is a strong solution, that is it satisfies the equation of evolution in the classical sense
Summary
A famous American zoologist of Swiss origin, Louis Agassiz, lived in the XIX century defined the barnacles like “little shrimps hanging from the rock with their heads, locked in a limestone house and kicked throwing food into their mouths”. The paper is organized as follows: we consider first that the boundary value of adults density is known and has some suitable properties In this way, we find the mild solution of the evolution problem for the adults density by means of affine semigroup techniques and successive approximation procedures. We find the mild solution of the evolution problem for the adults density by means of affine semigroup techniques and successive approximation procedures By using another successive approximation procedure, we find that the function which represents the boundary value of adults density belongs to a suitable Banach space which ensures that it has the requested properties. At the end we prove that this solution is the global strong solution of the system
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