Results 71 to 80 of about 59,515 (231)

On the well-posedness of the vacuum Einstein’s equations [PDF]

Journal of Evolution Equations, 2011
The Cauchy problem of the vacuum Einstein's equations aims to find a semi-metric $g_{ }$ of a spacetime with vanishing Ricci curvature $R_{ , }$ and prescribed initial data. Under the harmonic gauge condition, the equations $R_{ , }=0$ are transferred into a system of quasi-linear wave equations which are called the reduced Einstein equations ...
openaire   +4 more sources

On the deep‐water and shallow‐water limits of the intermediate long wave equation from a statistical viewpoint

Transactions of the London Mathematical Society, Volume 12, Issue 1, December 2025.
Abstract We study convergence problems for the intermediate long wave (ILW) equation, with the depth parameter δ>0$\delta > 0$, in the deep‐water limit (δ→∞$\delta \rightarrow \infty$) and the shallow‐water limit (δ→0$\delta \rightarrow 0$) from a statistical point of view.
Guopeng Li, Tadahiro Oh, Guangqu Zheng
wiley   +1 more source

Characterization of well-posedness of piecewise linear systems [PDF]

, 1998
One of the basic issues in the study of hybrid systems is the well-posedness (existence and uniqueness of solutions) problem of discontinuous dynamical systems. This paper addresses this problem for a class of piecewise-linear discontinuous systems under
Imura, J.-I., Schaft, A.J. van der
core   +2 more sources

Effective Macroscopic Equations for Biological Fluid and Nutrients' Transport in Vascularized Tumors Growing Via Proliferation and Chemotaxis

Mathematical Methods in the Applied Sciences, Volume 48, Issue 14, Page 13285-13299, 30 September 2025.
ABSTRACT This paper presents a system of partial differential equations designed to model fluid and nutrient transport within the growing tumor microenvironment. The fluid phase, representing both cells and extracellular fluids flowing within the interstitial space, is assumed to be intrinsically incompressible, so that growth can be modeled as a ...
Francesca Ballatore, Chiara Giverso, Raimondo Penta   +2 more
wiley   +1 more source

Vortex filament solutions of the Navier-Stokes equations

, 2020
We consider solutions of the Navier-Stokes equations in $3d$ with vortex filament initial data of arbitrary circulation, that is, initial vorticity given by a divergence-free vector-valued measure of arbitrary mass supported on a smooth curve.
Bedrossian, Jacob, Germain, Pierre, Harrop-Griffiths, Benjamin   +2 more
core  

Remark on well-posedness and ill-posedness for the KdV equation

Electronic Journal of Differential Equations, 2010
We consider the Cauchy problem for the KdV equation with low regularity initial data given in the space $H^{s,a}(mathbb{R})$, which is defined by the norm $$ | varphi |_{H^{s,a}}=| langle xi angle^{s-a} |xi|^a widehat{varphi} |_{L_{xi}^2}.
Takamori Kato
doaj  

On the Well-Posedness Concept in the Sense of Tykhonov

Journal of Optimization Theory and Applications, 2019
We introduce a general concept of well-posedness in the sense of Tykhonov for abstract problems formulated on metric spaces and characterize it in terms of properties for a family of approximating sets. Then, we illustrate these results in the study of some relevant particular problems with history-dependent operators: a fixed point problem, a ...
Mircea Sofonea, Mircea Sofonea, Yi-bin Xiao   +2 more
openaire   +2 more sources

Generalized φ‐Pullback Attractors in Time‐Dependent Spaces: Application to a Nonautonomous Wave Equation With Time‐Dependent Propagation Velocity

Mathematical Methods in the Applied Sciences, Volume 48, Issue 14, Page 13456-13474, 30 September 2025.
ABSTRACT We present sufficient conditions to obtain a generalized (φ,D)$$ \left(\varphi, \mathfrak{D}\right) $$‐pullback attractor for evolution processes on time‐dependent phase spaces, where φ$$ \varphi $$ is a given decay function and D$$ \mathfrak{D} $$ is a given universe.
Matheus Cheque Bortolan, Carlos Pecorari Neto, Heraclio López Lázaro, Paulo N. Seminario Huertas   +3 more
wiley   +1 more source

Well-posedness and stationary solutions [PDF]

, 2011
In this paper we prove existence and uniqueness of variational inequality solutions for a bistable quasilinear parabolic equation arising in the theory of solid-solid phase transitions and discuss its stationary solutions, which can be ...
Burns, Martin, Grinfeld, Michael
core  

Generalized Well-Posedness for Symmetric Vector Quasi-Equilibrium Problems

Journal of Applied Mathematics, 2015
We introduce and study well-posedness in connection with the symmetric vector quasi-equilibrium problem, which unifies its Hadamard and Levitin-Polyak well-posedness.
Wei-bing Zhang, Nan-jing Huang, Donal O’Regan   +2 more
doaj   +1 more source