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Complexity, 2020 The paper deals with the study of the existence of weak positive solutions for a new class of the system of elliptic differential equations with respect to the symmetry conditions and the right hand side which has been defined as multiplication of two ...
Youcef Bouizem +2 more
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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.
europepmc +2 more sources
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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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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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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Global Limit Theorem for Parabolic Equations with a Potential [PDF]
SIAM Journal on Mathematical Analysis, 2021 We obtain the asymptotics, as t + |x| → ∞, of the fundamental solution to the heat equation with a compactly supported potential. It is assumed that the corresponding stationary operator has at least one positive eigenvalue.
L. Koralov, B. Vainberg
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Open Mathematics, 2021 A nonlinear viscoelastic wave equation with Balakrishnan-Taylor damping and distributed delay is studied. By the energy method we establish the general decay rate under suitable hypothesis.
Choucha Abdelbaki +2 more
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Non-Degeneracy of Peak Solutions to the Schrödinger–Newton System
Advanced Nonlinear Studies, 2021 We are concerned with the following Schrödinger–Newton problem:
Guo Qing, Xie Huafei
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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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