TY - JOUR
T1 - Existence and uniqueness of solutions for a diffusion model of host-parasite dynamics
AU - Langlais, Michel
AU - Milner, Fabio Augusto
N1 - Funding Information:
* Corresponding author. E-mail address: milner@math.purdue.edu (F.A. Milner). 1 The work of this author was supported in part by NSF through grant No. INT-9415775.
PY - 2003/3/15
Y1 - 2003/3/15
N2 - Milner and Patton (J. Comput. Appl. Math., in press) introduced earlier a new approach to modeling host-parasite dynamics through a convection-diffusion partial differential equation, which uses the parasite density as a continuous structure variable. A motivation for the model was presented there, as well as results from numerical simulations and comparisons with those from other models. However, no proof of existence or uniqueness of solutions to the new model proposed was included there. In the present work the authors deal with the well posedness of that model and they prove existence and uniqueness of solutions, as well as establishing some asymptotic results.
AB - Milner and Patton (J. Comput. Appl. Math., in press) introduced earlier a new approach to modeling host-parasite dynamics through a convection-diffusion partial differential equation, which uses the parasite density as a continuous structure variable. A motivation for the model was presented there, as well as results from numerical simulations and comparisons with those from other models. However, no proof of existence or uniqueness of solutions to the new model proposed was included there. In the present work the authors deal with the well posedness of that model and they prove existence and uniqueness of solutions, as well as establishing some asymptotic results.
KW - Diffusion models
KW - Existence and uniqueness
KW - Host-parasite models
KW - Size-structured population models
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U2 - 10.1016/S0022-247X(03)00020-9
DO - 10.1016/S0022-247X(03)00020-9
M3 - Article
AN - SCOPUS:0038182931
SN - 0022-247X
VL - 279
SP - 463
EP - 474
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
ER -