Adaptation and fatigue model for neuron networks and large time asymptotics in a nonlinear fragmentation equation. [PDF]
J Math Neurosci, 2014 Motivated by a model for neural networks with adaptation and fatigue, we study a conservative fragmentation equation that describes the density probability of neurons with an elapsed time s after its last discharge.
Pakdaman K, Perthame B, Salort D.
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Fast rotation limit for the 2-D non-homogeneous incompressible Euler equations [PDF]
Journal of Mathematical Analysis and Applications, 2021 In the present paper, we study the fast rotation limit for the density-dependent incompressible Euler equations in two space dimensions with the presence of the Coriolis force.
Gabriele Sbaiz
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Selection–mutation dynamics with asymmetrical reproduction kernels [PDF]
Nonlinear Analysis, 2021 We study a family of selection-mutation models of a sexual population structured by a phenotypical trait. The main feature of these models is the asymmetric trait heredity or fecundity between the parents : we assume that each individual inherits mostly ...
B. Perthame +2 more
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On global existence for semilinear wave equations with space-dependent critical damping [PDF]
Journal of the Mathematical Society of Japan, 2021 The global existence for semilinear wave equations with space-dependent critical damping ∂ t u−∆u+ V0 |x| ∂tu = f(u) in an exterior domain is dealt with, where f(u) = |u|p−1u and f(u) = |u| are in mind.
M. Sobajima
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On the asymptotic behavior of a size-structured model arising in population dynamics
Malaya Journal of Matematik, 2023 We study the asymptotic behavior of a semilinear size-structured population model withdelay when the nonlinearity is small in some sense. The novelty in this work is that theoperator governing the linear part of the equation does not generate a compact ...
Nadia Drisi +3 more
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Double bubbles with high constant mean curvatures in Riemannian manifolds [PDF]
Nonlinear Analysis, 2021 We obtain existence of double bubbles of large and constant mean curvatures in Riemannian manifolds. These arise as perturbations of geodesic standard double bubbles centered at critical points of the ambient scalar curvature and aligned along eigen ...
Gianmichele Di Matteo, A. Malchiodi
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Coupled and uncoupled sign-changing spikes of singularly perturbed elliptic systems [PDF]
Communications in Contemporary Mathematics, 2021 We study the existence and asymptotic behavior of solutions having positive and sign-changing components to the singularly perturbed system of elliptic equations in a bounded domain Ω in R N , with N ≥ 4, ε > 0, µ i > 0, λ ij = λ ji < 0, α ij , β ij > 1,
M. Clapp, M. Soares
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Asymptotic stability analysis of Riemann-Liouville fractional stochastic neutral differential equations [PDF]
Miskolc Mathematical Notes, 2021 The novelty of our paper is to establish results on asymptotic stability of mild solutions in pth moment to Riemann-Liouville fractional stochastic neutral differential equations (for short Riemann-Liouville FSNDEs) of order α ∈ ( 2 ,1) using a Banach’s ...
Arzu Ahmadova, N. Mahmudov
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The evolution to equilibrium of solutions to nonlinear Fokker-Planck equation [PDF]
Indiana University Mathematics Journal, 2019 One proves the $H$-theorem for mild solutions to a nondegenerate, nonlinear Fokker-Planck equation $$ u_t-\Delta\beta(u)+\mathrm{ div}(D(x)b(u)u)=0, \ t\ge0, \ x\in\mathbb{R}^d,\hspace{1cm} (1)$$ and under appropriate hypotheses on $\beta,$ $D$ and $b ...
V. Barbu, M. Rockner
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On a system of multi-component Ginzburg-Landau vortices
Advances in Nonlinear Analysis, 2023 We study the asymptotic behavior of solutions for nn-component Ginzburg-Landau equations as ε→0\varepsilon \to 0. We prove that the minimizers converge locally in any Ck{C}^{k}-norm to a solution of a system of generalized harmonic map equations.
Hadiji Rejeb, Han Jongmin, Sohn Juhee
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