Results 21 to 30 of about 117 (94)
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
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Qualitative analysis for the nonlinear fractional Hartree type system with nonlocal interaction
Advances in Nonlinear Analysis, 2021 In the present paperwe study the existence of nontrivial solutions of a class of static coupled nonlinear fractional Hartree type system. First, we use the direct moving plane methods to establish the maximum principle(Decay at infinity and Narrow region
Wang Jun
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International Journal of Differential Equations, Volume 2025, Issue 1, 2025.The mathematical models of problems that arise in many branches of science are nonlinear equations of evolution (NLEE). For this reason, NLEE have served as a language in formulating many engineering and scientific problems. Although the origin of nonlinear evolution equations dates back to ancient times, significant developments have been made in ...
Murat Koparan, Salim A. Messaoudi
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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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Journal of Applied Mathematics, Volume 2025, Issue 1, 2025.We investigate the initial value problem associated to the higher order nonlinear Schrödinger equation i∂tu+−1j+1∂x2ju=u2ju x,t≠0∈ℝ,ux,0=u0x, where j ≥ 2 is any integer, u is a complex valued function, and the initial data u0 is real analytic on ℝ and has a uniform radius of spatial analyticity σ0 in the space variable.
Tegegne Getachew +3 more
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Advances in Nonlinear AnalysisThe Maxwell-Bloch system of equations with inhomogeneous broadening is studied, and the local and global well-posedness of the corresponding initial-boundary value problem is established by taking advantage of the integrability of the system and making ...
Biondini Gino +2 more
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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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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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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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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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