Results 31 to 40 of about 40,292 (276)

A Subelliptic Analogue of Aronson-Serrin's Harnack Inequality [PDF]

, 2012
We show that the Harnack inequality for a class of degenerate parabolic quasilinear PDE $$\p_t u=-X_i^* A_i(x,t,u,Xu)+ B(x,t,u,Xu),$$ associated to a system of Lipschitz continuous vector fields $X=(X_1,...,X_m)$ in in $\Om\times (0,T)$ with $\Om \subset
Capogna, Luca, Citti, Giovanna, Rea, Garrett   +2 more
core   +3 more sources

Two ground-state modifications of quantum-dot beryllium

, 2002
Exact electronic properties of a system of four Coulomb-interacting two-dimensional electrons in a parabolic confinement are reported. We show that degenerate ground states of this system are characterized by qualitatively different internal electron ...
A. Harju, A. Matulis, A.V. Filinov, B. Reusch, C. Yannouleas, C.E. Creffield, F. Bolton, F. Pederiva, K. Varga, P.A. Maksym, R. Egger, R. Egger, S. A. Mikhailov, S. Akbar, S.A. Mikhailov, S.A. Mikhailov, S.M. Reimann, U. Merkt, V. Fock, V.M. Bedanov, W. Häusler   +20 more
core   +1 more source

Supercritical degenerate parabolic-parabolic Keller-Segel system -- existence criterion given by the best constant in Sobolev's inequality

, 2018
This article presents a relationship between the sharp constant of the Sobolev inequality and the initial criterion to the global existence of degenerate parabolic-parabolic Keller-Segel system with the diffusion exponent $\frac{2n}{2+n}
Chen, Li, Li, Yue, Wang, Jinhuan
core   +1 more source

Hölder–Zygmund estimates for degenerate parabolic systems

Journal of Differential Equations, 2014
We consider energy solutions of the inhomogeneous parabolic $p$-Laplacien system $\partial_t u-\text{div}(|D u|^{p-2}D u)=-\text{div} g$. We show in the case $p\geq 2$ that if the right hand side $g$ is locally in $L^\infty(\text{BMO})$, then $u$ is locally in $L^\infty(\mathcal{C}^1)$, where $\mathcal{C}^1$ is the 1-H lder--Zygmund space. This is the
openaire   +3 more sources

Stationary Flows of the Parabolic Potential Barrier in Two Dimensions

, 2000
In the two-dimensional isotropic parabolic potential barrier $V(x, y)=V_0 -m\gamma^2 (x^2+y^2)/2$, though it is a model of an unstable system in quantum mechanics, we can obtain the stationary states corresponding to the real energy eigenvalue $V_0 ...
Abramov A A, Atabek O, Balazs N L, Barton G, Batchelor G K, Bialynicki-Birula I, Briet P, Castagnino M, Connor J N L, de Broglie L, Dirac P A M, Dirac P A M, Dirac P A M, Dirac P A M, Dirac P A M, Dirac P A M, Exner P, Feynman R P, Ford K W, Hirschfelder J O, Hirschfelder J O, Kobayashi T, Kobayashi T, Lamb H, Landau L D, Landau L D, Madelung E, Moiseyev N, Onsager L, Plotnikov V G, Rowley N, Sakurai J J, Schönberg M, Shimbori T, Shimbori T, Takabayasi T, Takabayasi T, Toshiki Shimbori, Tsunehiro Kobayashi   +38 more
core   +2 more sources

On a degenerate parabolic system

Journal of Differential Equations, 2008
The author considers a degenerate parabolic system \[ U_t-\Delta (|U|^{m-1}U)=0, \] where \(U(x, t)=(u_1, u_2, \cdots, u_l)\) is a vector function and \(m>1\). The system can be derived from a time-dependent p-curl system which describes Bean's critical-state model in the superconductivity theory.
openaire   +2 more sources

Al–Cu Composite Casting of Laser‐Deoxidized Copper: Bonding, Interfacial Chemistry, and Thermal Conductivity

Advanced Engineering Materials, EarlyView.
This study investigates laser‐based oxide removal of Cu inserts in oxygen‐free conditions and examines long‐term oxidation kinetics and surface chemistry under different atmospheres via X‐ray photoelectron spectroscopy. Al–Cu compound casting with differently oxidized surfaces is performed, and intermetallic phase formation, morphology, and thermal ...
Timon Steinhoff, Finn‐Lennard Janthur, Sascha Zimmermann, Sarah Seffer, Jörg Hermsdorf, René Gustus, Ludger Overmeyer, Wolfgang Maus‐Friedrichs, Hans Jürgen Maier, Christian Klose   +9 more
wiley   +1 more source

Hölder estimates for nonlinear degenerate parabolic sytems.

Journal für die reine und angewandte Mathematik (Crelles Journal), 1985
It is shown that for any weak solution of the nonlinear degenerate parabolic system \[ \partial u^ i/\partial t-div(|\nabla u|^{p-2}\nabla u^ i)=F_ i(x,t,\nabla u)\quad (i=1,...,m) \] in \(\Omega\times (0,T)\) when \(u=(u^ 1,...,u^ m)\), \(\Omega\subset {\mathbb{R}}^ n\), \(p>\max\{1,2N/(N+2)\},\) the spatial gradient \(\nabla u\) is Hölder continuous ...
Friedman, Avner, DiBenedetto, Emmanuele
openaire   +1 more source

Dynamics of Non-Autonomous Stochastic Semi-Linear Degenerate Parabolic Equations with Nonlinear Noise

Mathematics, 2023
In the present paper, we aim to study the long-time behavior of a stochastic semi-linear degenerate parabolic equation on a bounded or unbounded domain and driven by a nonlinear noise.
Xin Liu, Yanjiao Li
doaj   +1 more source

Productivity‐Driven Optimization of Laser Powder Bed Fusion Parameters for IN718 Superalloy: Process Control, Microstructure, and Mechanical Properties

Advanced Engineering Materials, EarlyView.
This study demonstrates how optimizing laser power, scanning speed, and hatching distance in laser powder bed fusion can boost the productivity of Inconel 718 manufacturing by up to 29% while maintaining mechanical integrity. The work delivers a validated process window and cost–time analysis, offering industry‐ready guidelines for efficient additive ...
Amir Behjat, Guido Barale, John Stavridis, Ehsan Norouzi, Jin‐Yoo Suh, Dong‐Ik Kim, Luca Iuliano, Abdollah Saboori   +7 more
wiley   +1 more source