We are interested in the long time behaviour of the positive solutions of the Cauchy problem involving the integro-differential equation
$\partial_t u(t,x)\\=\int_{\Omega }m(x,y)\left(u(t,y)-u(t,x)\right)\,dy+\left(a(x)-\int_{\Omega }k(x,y)u(t,y)\,dy\right)u(t,x),$
supplemented by the initial condition
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Figure 1.
Numerical approximation of the solution to (10) at different times for two configurations, in which only the mutation rate differs. The competition rate is constant and set to
Figure 2.
Numerical approximation of the solution of problem (10)-(11) at different times for two configurations, which differ only in their initial datum. The mutation and competition rates are constant and set respectively to
Figure 3.
Numerical approximation of the solution of problem (10)-(11) at different times. The mutation and competition rates are constant and set respectively to
Figure 4.
Numerical approximation of the solution of problem (10)-(11) at different times. The mutation and competition rates are constant and set respectively to
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