Results 91 to 100 of about 18,832,328 (177)

The Periodic Boundary Value Problem for the Weakly Dissipative μ-Hunter-Saxton Equation

Advances in Mathematical Physics, 2015
We study the periodic boundary value problem for the weakly dissipative μ-Hunter-Saxton equation. We establish the local well-posedness in Besov space B2,13/2, which extends the previous regularity range to the critical case.
Zhengyong Ouyang, Xiangdong Wang, Haiwu Rong   +2 more
doaj   +1 more source

Solvability and Boundedness in Chemotaxis‐Consumption Models With Oppositely Acting Nonlocal Sources

Mathematical Methods in the Applied Sciences, Volume 49, Issue 14, Page 16146-16162, 30 September 2026.
ABSTRACT In this paper, we investigate a chemotaxis system featuring a class of external source terms that incorporate both local and nonlocal growth as well as dampening effects. The model describes the evolution of a cell density u$$ u $$, which migrates in response to a chemical signal v$$ v $$, within an impermeable habitat.
Rafael Díaz Fuentes, Fatma Gamze Düzgün, Silvia Frassu, Giuseppe Viglialoro   +3 more
wiley   +1 more source

Hybrid Coupling With Operator Inference and the Overlapping Schwarz Alternating Method

International Journal for Numerical Methods in Engineering, Volume 127, Issue 17, 15 September 2026.
ABSTRACT This paper presents a hybrid approach for coupling subdomain‐local, nonintrusive Operator Inference (OpInf) reduced order models (ROMs) with each other and with subdomain‐local, high‐fidelity full order models (FOMs) using the overlapping Schwarz alternating method (O‐SAM).
Irina Tezaur, Eric Parish, Anthony Gruber, Ian Moore, Christopher Wentland, Alejandro Mota   +5 more
wiley   +1 more source

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  

Local well-posedness of the EPDiff equation: a survey

, 2017
International audienceThis article is a survey on the local well-posedness problem for the general EPDiff equation. The main contribution concerns recent results on local existence of the geodesics on $\mathrm{Diff}(\mathbb{T}^{d})$ and $\mathrm{Diff ...
Kolev, Boris
core   +1 more source

Local well-posedness for relaxational fluid vesicle dynamics

, 2018
We prove the local well-posedness of a basic model for relaxational fluid vesicle dynamics by a contraction mapping argument.
Köhne, Matthias, Matthias Köhne, Daniel Lengeler, Lengeler, Daniel   +3 more
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On well-posedness of energy supercritical NLS on product space Rn×T4−n ${\mathbb{R}}^{n}{\times}{\mathbb{T}}^{4-n}$ (n = 0, 1, 2, 3)

Advances in Nonlinear Analysis
We establish the well-posedness theory for the quintic nonlinear Schrödinger equation (NLS) on four-dimensional tori (i.e., T4 ${\mathbb{T}}^{4}$ ), which is an energy-supercritical model. Compared to the recent breakthrough work (B. Kwak and S.
Wang Han, Li Xing, Lyu Ziyue, Zhao Zehua, Zhou Wenyu   +4 more
doaj   +1 more source

On the Cauchy-problem for generalized Kadomtsev-Petviashvili-II equations

Electronic Journal of Differential Equations, 2009
The Cauchy-problem for the generalized Kadomtsev-Petviashvili-II equation $$ u_t + u_{xxx} + partial_x^{-1}u_{yy}= (u^l)_x, quad l ge 3, $$ is shown to be locally well-posed in almost critical anisotropic Sobolev spaces.
Axel Gruenrock
doaj  

The Robin Problems in the Coupled System of Wave Equations on a Half-Line

Axioms
This article investigates the local well-posedness of a coupled system of wave equations on a half-line, with a particular emphasis on Robin boundary conditions within Sobolev spaces.
Po-Chun Huang, Bo-Yu Pan
doaj   +1 more source

ε-solutions for quasi-variationalinequalities

, 2007
Approximate solutions for quasi-variational inequalities and for vector quasi-variationalinequalities have been recently investigated by the speaker.In this talk, we introduce and analyze the corresponding concepts of well-posedness and discuss about the
LIGNOLA, MARIA BEATRICE
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