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- W2558662820 abstract "This work deals with the existence and non-existence of travelling wave solutions for a two-dimensional reaction-diffusion equation coupled with ordinary differential equations. The system models the spatial spread of a fungal disease over a field of crops whose spatial configuration exhibits a periodic stripe pattern, such as a vineyard. The standard comparison principle does not hold for this system. We establish a sharp criterion for the existence of (directional) travelling waves in terms of what we call the epidemic threshold ({mathscr {R}}_0), which is independent of the direction of the travelling wave. We then study the minimal speed (c^*_theta ) of travelling waves for each direction (theta in [0,2pi )) and prove its monotone dependence on (theta ). Our analysis is based on the fixed point argument, a variational characterization of principal eigenvalues and Harnack type inequalities for elliptic and parabolic problems." @default.
- W2558662820 created "2016-12-08" @default.
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- W2558662820 date "2016-01-01" @default.
- W2558662820 modified "2023-09-30" @default.
- W2558662820 title "Plant Disease Propagation in a Striped Periodic Medium" @default.
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- W2558662820 doi "https://doi.org/10.1007/978-81-322-3640-5_8" @default.
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