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We study acceleration phenomena in monostable integro-differential equations with ignition nonlinearity. Our results cover fractional Laplace operators and standard convolutions in a unified way, which is also a contribution of this paper. To achieve this, we construct a sub-solution that captures the expected dynamics of the accelerating solution, and this is here the main difficulty. This study involves the flattening effect occurring in accelerated propagation phenomena.
We present and analyse a novel manifestation of the revival phenomenon for linear spatially periodic evolution equations, in the concrete case of three nonlocal equations that arise in water wave theory and are defined by convolution kernels. Revival
In this work we prove the uniqueness of solutions to the nonlocal linear equation $L varphi - c(x)varphi = 0$ in $mathbb{R}$, where $L$ is an elliptic integro-differential operator, in the presence of a positive solution or of an odd solution vanishi
This is the first of two papers concerning saddle-shaped solutions to the semilinear equation $L_K u = f(u)$ in $mathbb{R}^{2m}$, where $L_K$ is a linear elliptic integro-differential operator and $f$ is of Allen-Cahn type. Saddle-shaped solutions
Generalized summability results are obtained regarding formal solutions of certain families of linear moment integro-differential equations with time variable coefficients. The main result leans on the knowledge of the behavior of the moment derivati
Via Carleman estimates we prove uniqueness and continuous dependence results for lateral Cauchy problems for linear integro-differential parabolic equations without initial conditions. The additional information supplied prescribes the conormal deriv