Results 61 to 70 of about 3,079 (223)
Normalized solutions to nonautonomous Kirchhoff equation
Communications in Analysis and Mechanics<p>In this paper, we studied the existence of normalized solutions to the following Kirchhoff equation with a perturbation:</p><p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \left\{ \begin{aligned} &-\left(a+b\int _{\mathbb{R}^{N}}\left | \nabla u \right|^{2} dx\right)\Delta u+\lambda u =
Xin Qiu, Zeng Qi Ou, Ying Lv
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Advanced Optical Materials, EarlyView.A theoretical model is developed to visualize three‐dimensional refractive index profiles in transmission holographic gratings. In this work, it is applied to photopolymerizable hydrogels, enabling detailed analysis of the internal structure of recorded holograms and their evolution under different degradation conditions.
Belén Nieto‐Rodríguez +4 more
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Boundary Value Problems, 2021 A nonlinear viscoelastic Kirchhoff-type equation with Balakrishnan–Taylor damping and distributed delay is studied. By the energy method we establish the general decay rate under suitable hypothesis.
Abdelbaki Choucha, Salah Boulaaras
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Existence and uniqueness of normalized solutions for the Kirchhoff equation
Applied Mathematics Letters, 2017 For a class of Kirchhoff functional, we first give a complete classification with respect to the exponent $p$ for its $L^2$-normalized critical points, and show that the minimizer of the functional, if exists, is unique up to translations. Secondly, we search for the mountain pass type critical point for the functional on the $L^2$-normalized manifold,
Xiaoyu Zeng, Yimin Zhang
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Hard‐Magnetic Soft Millirobots in Underactuated Systems
Advanced Robotics Research, EarlyView.This review provides a comprehensive overview of hard‐magnetic soft millirobots in underactuated systems. It examines key advances in structural design, physics‐informed modeling, and control strategies, while highlighting the interplay among these domains.
Qiong Wang +4 more
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A Review on Sensor Technologies, Control Approaches, and Emerging Challenges in Soft Robotics
Advanced Robotics Research, EarlyView.This review provides an introspective of sensors and controllers in soft robotics. Initially describing the current sensing methods, then moving on to the control methods utilized, and finally ending with challenges and future directions in soft robotics focusing on the material innovations, sensor fusion, and embedded intelligence for sensors and ...
Ean Lovett +5 more
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Stability and critical dimension for Kirchhoff systems in closed manifolds
Advanced Nonlinear StudiesThe Kirchhoff equation was proposed in 1883 by Kirchhoff [Vorlesungen über Mechanik, Leipzig, Teubner, 1883] as an extension of the classical D’Alembert’s wave equation for the vibration of elastic strings. Almost one century later, Jacques Louis Lions [“
Hebey Emmanuel
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The Existence of Multiple Solutions for Nonhomogeneous Kirchhoff Type Equations in
Abstract and Applied Analysis, 2013 We are concerned with the existence of multiple solutions to the nonhomogeneous Kirchhoff type equation where are positive constants, , we can find a constant such that for all the equation has at least two radial solutions provided .
Qi Zhang, Xiaoli Zhu
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Asymptotic Limits for Mildly Degenerate Kirchhoff Equations [PDF]
SIAM Journal on Mathematical Analysis, 2013 We study the asymptotic behavior of the solutions of the mildly degenerate Kirchhoff equation with a dissipative term. We obtain a new estimate on second-in-time derivative of the solution. Moreover we renormalize the solution in such a way that the renormalization as a no zero limit as t goes to infinity.
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Neuromorphic Near‐Sensor and In‐Sensor Computing Enabled by Next‐Generation Material‐Based Sensors
Advanced Science, EarlyView.This Review presents a structural framework that classifies neuromorphic sensing into near‐sensor and in‐sensor architectures, clarifying physical coupling between sensing and computation. The framework connects neural and synaptic device functions with recent advances in optical, mechanical, and chemical sensing, compares energy consumption and ...
Su Yeon Jung +7 more
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