Results 31 to 40 of about 1,347,601 (289)
On the structure of minimizers of causal variational principles in the non-compact and equivariant settings [PDF]
, 2012 We derive the Euler-Lagrange equations for minimizers of causal variational principles in the non-compact setting with constraints, possibly prescribing symmetries.
Finster, Felix, Bernard, Yann
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Lagrangian description of the variational equations [PDF]
Chaos, Solitons & Fractals, 2003 A variant of the usual Lagrangian scheme is developed which describes both the equations of motion and the variational equations of a system. The required (prolonged) Lagrangian is defined in an extended configuration space comprising both the original configurations of the system and all the virtual displacements joining any two integral curves.
Arizmendi, C. M. +3 more
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Variational Integrals of a Class of Nonhomogeneous 𝒜-Harmonic Equations
Abstract and Applied Analysis, 2014 We introduce a class of variational integrals whose Euler equations are nonhomogeneous 𝒜-harmonic equations. We investigate the relationship between the minimization problem and the Euler equation and give a simple proof of the existence of some ...
Guanfeng Li, Yong Wang, Gejun Bao
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Noncommutative variations on Laplace’s equation [PDF]
Analysis & PDE, 2008 As a first step at developing a theory of noncommutative nonlinear elliptic partial differential equations, we analyze noncommutative analogues of Laplace's equation and its variants (some of the them nonlinear) over noncommutative tori. Along the way we prove noncommutative analogues of many results in classical analysis, such as Wiener's Theorem on ...
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Variational quantum evolution equation solver
Scientific Reports, 2022 AbstractVariational quantum algorithms offer a promising new paradigm for solving partial differential equations on near-term quantum computers. Here, we propose a variational quantum algorithm for solving a general evolution equation through implicit time-stepping of the Laplacian operator.
Fong Yew Leong +2 more
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Asymptotic Methods for Solitary Solutions and Compactons
Abstract and Applied Analysis, 2012 This paper is an elementary introduction to some new asymptotic methods for the search for the solitary solutions of nonlinear differential equations, nonlinear differential-difference equations, and nonlinear fractional differential equations ...
Ji-Huan He
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Variational equations with constraints
Applied Mathematics Letters, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Asymptotic Variational Wave Equations [PDF]
Archive for Rational Mechanics and Analysis, 2006 The initial boundary value problem for the equation \((u_{t}+f(u)_{x})_{x}=\frac{1}{2}f''(u)u_{x}^2\) on \((0,T)\times \mathbb{R}^{+}\) is investigated. The authors prove that conservative solutions can be globally defined. Under non-degeneracy condition the conservative solution is unique.
Bressan, Alberto +2 more
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Variational Methods for Nonsmooth Mechanics [PDF]
, 2003 In this thesis we investigate nonsmooth classical and continuum mechanics and its discretizations by means of variational numerical and geometric methods.
Fetecau, Razvan Constantin
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A variational theory of the Hessian equation
Communications on Pure and Applied Mathematics, 2001 AbstractBy studying a negative gradient flow of certain Hessian functionals we establish the existence of critical points of the functionals and consequently the existence of ground states to a class of nonhomogenous Hessian equations. To achieve this we derive uniform, first‐ and second‐order a priori estimates for the elliptic and parabolic Hessian ...
Chou, Kai-Seng, Wang, Xu-Jia
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