Chase-and-Run and Chirality in Nonlocal Models of Pattern Formation. [PDF]
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Perturbed Nonlocal Stochastic Functional Differential Equations
Qualitative Theory of Dynamical Systems, 2020The authors discuss the asymptotic behavior of the solution for a class of perturbed nonlocal stochastic functional differential equations. They evaluate the distance between the latter and of the unperturbed solution, in finite time-intervals, and on maximal intervals as the small perturbations tend to zero. These results non-trivially extend previous
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Rocky Mountain Journal of Mathematics, 2022The paper is focused on the nonlocal fractional differential equation with an initial condition \[ \left\{\begin{array}{l}\displaystyle\frac{d}{dt}\left[k*(u-u_0)\right](t)+Au(t)=f(t,u(t)),\,\,\,t>0,\\ u(0)=u_0, \end{array}\right.\tag{1} \] where \(u:[0,\infty)\to H\) is the unknown function, \(H\) is a separable Hilbert space, the kernel \(k\in L_ ...
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