Attractors of semigroups associated with nonlinear systems for diffusive phase separation
Abstract and Applied Analysis, Volume 1, Issue 2, Page 169-192, 1996., 1996 We consider a model for diffusive phase transitions, for instance, the component separation in a binary mixture. Our model is described by two functions, the absolutete temperature θ : = θ(t, x) and the order parameter w : = w(t, x), which are governed by a system of two nonlinear parabolic PDEs.
Nobuyuki Kenmochi
wiley +1 more source
Normalized solutions for a class of scalar field equations involving mixed fractional Laplacians
Advanced Nonlinear Studies, 2022 The purpose of this article is to establish sharp conditions for the existence of normalized solutions to a class of scalar field equations involving mixed fractional Laplacians with different orders.
Luo Tingjian, Hajaiej Hichem
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On the derivation of the wave kinetic equation for NLS
Forum of Mathematics, Pi, 2021 A fundamental question in wave turbulence theory is to understand how the wave kinetic equation describes the long-time dynamics of its associated nonlinear dispersive equation.
Yu Deng, Zaher Hani
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Singularly perturbed Choquard equations with nonlinearity satisfying Berestycki-Lions assumptions
Advances in Nonlinear Analysis, 2019 In the present paper, we consider the following singularly perturbed problem:
Tang Xianhua, Chen Sitong
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Nehari-type ground state solutions for a Choquard equation with doubly critical exponents
Advances in Nonlinear Analysis, 2020 This paper deals with the following Choquard equation with a local nonlinear perturbation:
Chen Sitong, Tang Xianhua, Wei Jiuyang
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Advances in Nonlinear Analysis, 2018 In even space dimensions, the initial value problems for some high-order focusing semilinear evolution equations with exponential nonlinearities are considered.
Saanouni Tarek
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Effects of Brownian noise strength on new chiral solitary structures
Journal of Low Frequency Noise, Vibration and Active Control, 2023 In this paper, we investigate the nonlinear Chiral Schrödinger equation (CNLSE) in two dimensions where noise term affected randomly with time. This equation characterized some edges states of fractional-Hall Effect features in quantum.
Yousef F Alharbi +2 more
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Nonlinear nonlocal elliptic problems in ℝ3: existence results and qualitative properties
Demonstratio MathematicaWe consider the following nonlinear nonlocal elliptic problem: −a+b∫R3∣∇ψ∣2dxΔψ+λψ=∫R3G(ψ(y))∣x−y∣αdyG′(ψ),x∈R3,-\left(a+b\mathop{\int }\limits_{{{\mathbb{R}}}^{3}}{| \nabla \psi | }^{2}{\rm{d}}x\right)\Delta \psi +\lambda \psi =\left(\mathop{\int ...
Lü Dengfeng, Dai Shu-Wei
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Unconditional uniqueness for the energy-critical nonlinear Schrödinger equation on $\mathbb {T}^{4}$
Forum of Mathematics, Pi, 2022 We consider the $\mathbb {T}^{4}$ cubic nonlinear Schrödinger equation (NLS), which is energy-critical. We study the unconditional uniqueness of solutions to the NLS via the cubic Gross–Pitaevskii hierarchy, an uncommon method for NLS analysis which is ...
Xuwen Chen, Justin Holmer
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Local minimizers for the NLS equation with localized nonlinearity on noncompact metric graphs
Open MathematicsWe investigate the existence of local minimizers for the nonlinear Schrödinger (NLS) equation with localized nonlinearity on noncompact metric graphs. In the absence of ground states, we prove that normalized local minimizers of the NLS equation do exist
Li Xiaoguang
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