Zobrazeno 1 - 10
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pro vyhledávání: '"45K05"'
We prove convergence of the nonlocal Allen-Cahn equation to mean curvature flow in the sharp interface limit, in the situation when the parameter corresponding to the kernel goes to zero fast enough with respect to the diffuse interface thickness. Th
Externí odkaz:
http://arxiv.org/abs/2410.08596
We study existence, uniqueness, norm estimates and asymptotic time behaviour (in some cases can be claimed to be sharp) for the solution of a general evolutionary integral (differential) equation of scalar type on a locally compact separable unimodul
Externí odkaz:
http://arxiv.org/abs/2409.18141
We study the regularity of weak solutions to nonlocal in time subdiffusion equations for a wide class of weakly singular kernels appearing in the generalised fractional derivative operator. We prove a weak Harnack inequality for nonnegative weak supe
Externí odkaz:
http://arxiv.org/abs/2409.04841
Autor:
Loher, Amélie
The purpose of this note is to demonstrate the announced result in [Loher, The Strong Harnack inequality for the Boltzmann equation, S\'eminaire Laurent Schwartz proceeding] by filling the gap in the proof sketch. We prove the semi-local Strong Harna
Externí odkaz:
http://arxiv.org/abs/2409.02903
Autor:
Chen, Yuming, Vougalter, Vitali
We consider some reaction-diffusion equations describing systems with the nonlocal consumption of resources and the intraspecific competition. Sharp conditions on the coefficients are obtained to ensure the stability and instability of nontrivial con
Externí odkaz:
http://arxiv.org/abs/2409.03191
Autor:
Anguelov, Roumen, Bright, Chelsea
We consider a nonlocal aggregation diffusion equation incorporating repulsion modelled by nonlinear diffusion and attraction modelled by nonlocal interaction. When the attractive interaction kernel is radially symmetric and strictly increasing on its
Externí odkaz:
http://arxiv.org/abs/2408.11921
Autor:
Bandini, Elena, Keller, Christian
We study the optimal control of path-dependent piecewise deterministic processes. An appropriate dynamic programming principle is established. We prove that the associated value function is the unique minimax solution of the corresponding non-local p
Externí odkaz:
http://arxiv.org/abs/2408.02147
Publikováno v:
J. Differential Equations, 2022, V.327, 418-447
In this paper, the asymptotic behavior of a semilinear heat equation with long time memory and non-local diffusion is analyzed in the usual set-up for dynamical systems generated by differential equations with delay terms. This approach is different
Externí odkaz:
http://arxiv.org/abs/2407.17923
Neural field equations with time-periodic external inputs and some applications to visual processing
Autor:
Bolelli, Maria Virginia, Prandi, Dario
The aim of this work is to present a mathematical framework for the study of flickering inputs in visual processing tasks. When combined with geometric patterns, these inputs influence and induce interesting psychophysical phenomena, such as the MacK
Externí odkaz:
http://arxiv.org/abs/2407.17294
Autor:
Cañizo, José A., Tassi, Niccolò
We study a nonlocal approximation of the Fokker-Planck equation in which we can estimate the speed of convergence to equilibrium in a way which respects the local limit of the equation. This uniform estimate cannot be easily obtained with standard in
Externí odkaz:
http://arxiv.org/abs/2407.03870