RT Journal Article
T1 Analysis of a mathematical model arising in plant disease epidemiology
A1 Bazarra Garcia, Noelia
A1 Colturato, Michele
A1 Fernández García, José Ramón
A1 Naso, Maria Grazia
A1 Simonetto, Anna
A1 Gilioli, Gianni
K1 12 Matemáticas
K1 1206 Análisis Numérico
K1 1299 Otras Especialidades Matemáticas
AB In this work we study from the mathematical and numerical point of view a problem arising in vector-borne plant diseases. The model is written as a nonlinear system composed of a parabolic partial differential equation for the vector abundance function and a first-order ordinary differential equation for the plant health function. An existence and uniqueness result is proved using backward finite differences, uniform estimates and passing to the limit. The regularity of the solution is also obtained. Then, using the finite element method and the implicit Euler scheme, fully discrete approximations are introduced. A discrete stability property and a main a priori error estimates result are proved using a discrete version of Gronwall’s lemma and some estimates on the different approaches. Finally, some numerical results, in one and two dimensions, are presented to demonstrate the accuracy of the approximation and the behaviour of the solution.
PB Applied Mathematics & Optimization
SN 00954616
YR 2022
FD 2022-04-19
LK http://hdl.handle.net/11093/3831
UL http://hdl.handle.net/11093/3831
LA eng
NO Applied Mathematics & Optimization, 85(19): (2022)
NO Financiado para publicación en acceso aberto: Universidade de Vigo/CISUG
NO Agencia Estatal de Investigación | Ref. PGC2018-096696-B-I00
DS Investigo
RD 18-abr-2025