Calculus of Variations and Geometric Measure Theory

N. Bazarra - M. Colturato - J. R. Fernandez - M. G. Naso - A. Simonetto - G. Gilioli

Analysis of a mathematical model arising in plant disease epidemiology

created by michele on 12 Aug 2022
modified on 10 Dec 2022


Published Paper

Inserted: 12 aug 2022
Last Updated: 10 dec 2022

Journal: App. Math. Opt.
Volume: 85
Number: 19
Pages: 28
Year: 2022
Doi: 10.1007/s00245-022-09858-z


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.

Keywords: finite elements, Physiologically-based models, Mechanistic model, Analysis of PDE, Kolmogorov Equation, parabolic nonlinear equation