The Maximal Regularity of Nonlinear Second-Order Hyperbolic Boundary Differential Equations
AxiomsIn this paper, we show the maximal regularity of nonlinear second-order hyperbolic boundary differential equations. We aim to show if the given second-order partial differential operator satisfies the specific ellipticity condition; additionally, if ...
Xingyu Liu
doaj +3 more sources
On the Relation of Delay Equations to First-Order Hyperbolic Partial Differential Equations [PDF]
, 2013 This paper establishes the equivalence between systems described by a single first-order hyperbolic partial differential equation and systems described by integral delay equations.
Karafyllis, Iasson, Krstic, Miroslav
core +1 more source
The Einstein-Friedrich-nonlinear scalar field system and the stability of scalar field Cosmologies [PDF]
, 2017 A frame representation is used to derive a first order quasi-linear symmetric hyperbolic system for a scalar field minimally coupled to gravity. This procedure is inspired by similar evolution equations introduced by Friedrich to study the Einstein-Euler
Alho, Artur +2 more
core +2 more sources
Local wellposedness of quasilinear Maxwell equations with absorbing boundary conditions [PDF]
, 2018 In this article we provide a local wellposedness theory for quasilinear Maxwell equations with absorbing boundary conditions in $\mathcal{H}^m$ for $m \geq 3$.
Schnaubelt, Roland, Spitz, Martin
core +3 more sources
Flux Limiter Methods in 3D Numerical Relativity [PDF]
, 2002 New numerical methods have been applied in relativity to obtain a numerical evolution of Einstein equations much more robust and stable. Starting from 3+1 formalism and with the evolution equations written as a FOFCH (first-order flux conservative ...
Bona, C., Palenzuela, C.
core +2 more sources
Integrable Abel equations and Vein's Abel equation [PDF]
, 2016 We first reformulate and expand with several novel findings some of the basic results in the integrability of Abel equations. Next, these results are applied to Vein's Abel equation whose solutions are expressed in terms of the third order hyperbolic ...
Mancas, Stefan C., Rosu, Haret C
core +3 more sources
Chemical Engineering Journal Advances, 2023 The tangent hyperbolic nanofluid behaviour is observed in multiple practical applications and extensively used in different laboratory experiments. It motivates to focus on the two-dimensional boundary layer flow of tangent hyperbolic nanofluid past a ...
Hiranmoy Maiti, Samir Kumar Nandy
doaj +1 more source
Einstein-Bianchi Hyperbolic System for General Relativity [PDF]
, 1997 By employing the Bianchi identities for the Riemann tensor in conjunction with the Einstein equations, we construct a first order symmetric hyperbolic system for the evolution part of the Cauchy problem of general relativity.
Anderson, Arlen +2 more
core +2 more sources
The First Integral Method to the Nonlinear Schrodinger Equations in Higher Dimensions
Abstract and Applied Analysis, 2013 The first integral method introduced by Feng is adopted for solving some important nonlinear partial differential equations, including the (2 + 1)-dimensional hyperbolic nonlinear Schrodinger (HNLS) equation, the generalized nonlinear Schrodinger (GNLS ...
Shoukry Ibrahim Atia El-Ganaini
doaj +1 more source
Bounder solution on a strip to a system of nonlinear hyperbolic equations with mixed derivatives
Қарағанды университетінің хабаршысы. Математика сериясы, 2016 The system of nonlinear hyperbolic equations with mixed derivatives is considered on the strip. Time variable of the unknown function changes on the whole axis, and the spatial variable belongs to a finite interval.
D.S. Dzhumabaev, S.M. Temesheva
doaj +1 more source