Results 201 to 210 of about 41,256 (237)

Kirchhoff equations with indefinite potentials

Applicable Analysis, 2021
In this paper we consider four-superlinear Kirchhoff equations. In contrast to most studies, we allowed the potential V is indefinite, precisely, the operator −Δ+V possesses a finite-dimensional ne...
Lin Li, Jiafa Xu
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Kirchhoff or wave equation?

SEG Technical Program Expanded Abstracts 2003, 2003
Wave equation (or wave field extrapolation) techniques have been used in industry for the past few years, with the purpose to improve the accuracy of 3D depth imaging over the conventional Kirchhoff migration. However, on many field data examples using different wave equation implementations from different processing shops, we have seen high-quality ...
Zhiming Li, Chen‐Bin Su, Wes Bauske, Sharma Tadepalli   +3 more
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Nonlinear perturbations of the kirchhoff equation

Communications on Pure and Applied Mathematics, 1994
The initial value problem \[ u_{tt} - \Bigl( 1+ \int_{\mathbb{R}^ n} | \nabla u |^ 2 dx \Bigr) \Delta u = F(u,u_ t, \nabla u), \quad u(0,x) = \varepsilon \Phi (x),\tag{*} \] \[ u_ t(0,x) = \varepsilon \psi (x),\quad \Phi, \psi \in C_ 0^ \infty (\mathbb{R}^ n), \] \(F\) being \(C^ \infty\), and \(F(\lambda) = O(| \lambda |^{u + 1})\) near \(\lambda = 0\)
D'ANCONA, Piero Antonio, S. SPAGNOLO
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Multiple Solutions for a Kirchhoff-Type Equation

Mediterranean Journal of Mathematics, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Pei, Ruichang, Ma, Caochuan
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One-dimensional Kirchhoff equation

Nonlinear Analysis: Theory, Methods & Applications, 2002
The paper deals with the Cauchy problem of the form \[ \begin{gathered} u_{tt} (x,t)-\gamma \left(\int^\infty_{-\infty} u^2_x(x,t)dx \right)u_{xx}(x,t) =0,\\ u(x,0)= \varphi(x),\;u_t(x,0) =\psi(x),\;x\in \mathbb{R},\end{gathered} \] where \(\gamma: [0,\infty)\to [0,\infty)\) is a given Lipschitz \(C^1\) function, \(\varphi \in C^3(\mathbb{R})\), \(\psi\
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Kirchhoff equations in $B^{k}_{\Delta}$ classes

Revista Matemática Complutense, 2009
The author studies the global solvability of the Cauchy problem for the Kirchhoff equation with non-ultradifferentiable initial data and forcing term. More precisely, he introduces the subclass \(B^k_\Delta\) of \[ H^{1+{k\over 2}}\times H^{{k\over 2}}\times L^1_{\text{loc}}([0,\infty); H^{{k\over 2}}) \] and proves for \(k= 1,2\) global existence and ...
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Orbital Stability of Nonlinear Schrödinger–Kirchhoff Equations

Mediterranean Journal of Mathematics, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Schrödinger–Kirchhoff equation involving double critical nonlinearities

Journal of Mathematical Analysis and Applications, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zuji Guo, Xinguang Zhang
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Multiple nontrivial solutions to a -Kirchhoff equation

Nonlinear Analysis: Theory, Methods & Applications, 2012
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Liu, Duchao, Zhao, Peihao
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3D Wave Equation Kirchhoff Migration

SEG Technical Program Expanded Abstracts 2012, 2012
Ehinger et al. (1996) described a method for performing prestack depth migration by computing Green’s functions from the surface with a wavefield extrapolation method and then using them in a frequency-dependent Kirchhoff migration. The primary benefit of this method is that one can sort the output of a wave equation migration by sourcereceiver offset,
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