@article{fdi:010079856, title = {{W}ell-posedness, positivity, and time asymptotics properties for a reaction-diffusion model of plankton communities, involving a rational nonlinearity with singularity}, author = {{P}erasso, {A}. and {R}ichard, {Q}uentin and {A}zzali, {I}. and {V}enturino, {E}.}, editor = {}, language = {{ENG}}, abstract = {{I}n this work, we consider a reaction-diffusion system, modeling the interaction between nutrients, phytoplankton, and zooplankton. {U}sing a semigroup approach in{L}2, we prove global existence, uniqueness, and positivity of the solutions. {T}he nonlinearity is handled by providing estimates in{L} infinity, allowing to deal with most of the functional responses that describe predator/prey interactions ({H}olling {I}, {II}, {III}, {I}vlev) in ecology. {T}he paper finally exhibits some time asymptotic properties of the solutions.}, keywords = {plankton modeling ; positivity ; predator-prey models ; reaction-diffusion models ; well-posedness}, booktitle = {}, journal = {{S}tudies in {A}pplied {M}athematics}, volume = {146}, numero = {1}, pages = {211--232}, ISSN = {0022-2526}, year = {2021}, DOI = {10.1111/sapm.12345}, URL = {https://www.documentation.ird.fr/hor/fdi:010079856}, }