Results 31 to 40 of about 41,256 (237)

Existence and Asymptotic Behavior of Ground State Solutions to Kirchhoff-Type Equations of General Convolution Nonlinearity with a Steep Potential Well

Mathematics, 2022
In this paper, we consider a new kind of Kirchhoff-type equation which is stated in the introduction. Under certain assumptions on potentials, we prove by variational methods that the equation has at least a ground state solution and investigate the ...
Li Zhou, Chuanxi Zhu
doaj   +1 more source

DISPERSION AND ASYMPTOTIC PROFILES FOR KIRCHHOFF EQUATIONS [PDF]

Topics in Contemporary Differential Geometry, Complex Analysis and Mathematical Physics, 2007
The aim of this article is to describe asymptotic profiles for the Kirchhoff equation, and to establish time decay properties and dispersive estimates for Kirchhoff equations. For this purpose, the method of asymptotic integration is developed for the corresponding linear equations and representation formulae for their solutions are obtained.
Matsuyama, Tokio, Ruzhansky, Michael
openaire   +2 more sources

A Sub-Supersolution Approach for a Quasilinear Kirchhoff Equation

, 2014
In this paper we establish an existence result for a quasilinear Kirchhoff equation via a sub and supersolution approach, by using the pseudomonotone operators ...
Alves, Claudianor O., Corrêa, Francisco Julio S. A.   +1 more
core   +1 more source

Generalized Kirchhoff Equations

IFAC Proceedings Volumes, 2000
Abstract Existing theories of control of autonomous underwater vehicle are based mainly on a potential framework for the surrounding fluid. It leads to ODE governing the motion of a vehicle. On the other hand an influence of more realistic rheology accounted for a different types of vorticity shedding can critically change the “potential” stability ...
openaire   +1 more source

On an elliptic Kirchhoff-type problem depending on two parameters

, 2009
In this paper, we consider the Dirichlet problem associated to an elliptic Kirchhoff-type equation depending on two parameters. Under rather general and natural assumptions, we prove that, for certain values of the parameters, the problem has at least ...
A. Mao, Biagio Ricceri, C.O. Alves, K. Perera, M. Chipot, T.F. Ma, X. He, Z.T. Zhang   +7 more
core   +2 more sources

The Kirchhoff gauge

, 2006
We discuss the Kirchhoff gauge in classical electrodynamics. In this gauge the scalar potential satisfies an elliptical equation and the vector potential satisfies a wave equation with a nonlocal source.
Brill, Heras, Heras, Heras, Itin, Jackson, Jackson, Jackson, José A. Heras, Kirchhoff, Kobe, Kobe, Rohrlich, Yang, Yang, Zampino   +15 more
core   +1 more source

Global well-posedness of Kirchhoff systems [PDF]

, 2012
The aim of this paper is to establish the $H^1$ global well-posedness for Kirchhoff systems. The new approach to the construction of solutions is based on the asymptotic integrations for strictly hyperbolic systems with time-dependent coefficients. These
Bernstein, Callegari, Coddington, DʼAncona, DʼAncona, DʼAncona, Ghisi, Greenberg, Hartman, Hirosawa, Kajitani, Manfrin, Manfrin, Matsuyama, Matsuyama, Matsuyama, Mizohata, Nishida, Nishihara, Ruzhansky, Rzymowski, Yamazaki, Yamazaki, Yamazaki, Yosida   +24 more
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Rafting of Ni‐Based Superalloys Under Multiaxial Load as Understood by Phase‐Field Simulations and Critical Experiments

Advanced Engineering Materials, EarlyView.
Phase‐field simulations coupled with dislocation‐density‐based crystal plasticity modeling reproduce γ′ rafting behavior in single‐crystal Ni‐based superalloys under varied loading conditions. The model captures both macroscopic creep and microscopic morphology evolution, with results matching high‐temperature creep experiments.
Micheal Younan, David Bürger, Gunther Eggeler, Oleg Shchyglo, Ingo Steinbach, Muhammad Adil Ali   +5 more
wiley   +1 more source

Global attractors for Kirchhoff wave equation with nonlinear damping and memory

Boundary Value Problems, 2020
In this paper, we prove that the existence of global attractors for a Kirchhoff wave equation with nonlinear damping and memory.
Suli Zhang, Jianwen Zhang, Haiyan Wang
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A multiplicity result for a fractional Kirchhoff equation in $\mathbb{R}^{N}$ with a general nonlinearity

, 2017
In this paper we deal with the following fractional Kirchhoff equation \begin{equation*} \left(p+q(1-s) \iint_{\mathbb{R}^{2N}} \frac{|u(x)- u(y)|^{2}}{|x-y|^{N+2s}} \, dx\,dy \right)(-\Delta)^{s}u = g(u) \mbox{ in } \mathbb{R}^{N}, \end{equation*} where
Ambrosio, Vincenzo, Isernia, Teresa
core   +1 more source