Results 71 to 80 of about 12,675 (193)

Higher integrability for obstacle problem related to the singular porous medium equation

Boundary Value Problems, 2020
In this paper we study the self-improving property of the obstacle problem related to the singular porous medium equation by using the method developed by Gianazza and Schwarzacher (J. Funct. Anal. 277(12):1–57, 2019).
Qifan Li
doaj   +1 more source

Regularizations of forward‐backward parabolic PDEs

GAMM-Mitteilungen, Volume 47, Issue 4, November 2024.
Abstract Forward‐backward parabolic equations have been studied since the 1980s, but a mathematically rigorous picture is still far from being established. As quite a number of new papers have appeared recently, we review in this work the current state of the art.
Carina Geldhauser
wiley   +1 more source

Flow relaxation method in solving quasilinear parabolic equations [PDF]

Компьютерные исследования и моделирование, 2011
This article proposes a numeric method of solution of quasilinear parabolic equations, based on the flux approximation, describes the implementation of the method on a rectangular grid and presents numerical results.
Alexey I. Lobanov, V. A. Usenko
doaj   +1 more source

Codimension two mean curvature flow of entire graphs

Journal of the London Mathematical Society, Volume 110, Issue 5, November 2024.
Abstract We consider the graphical mean curvature flow of maps f:Rm→Rn$\mathbf {f}:{\mathbb {R}^{m}}\rightarrow {\mathbb {R}^{n}}$, m⩾2$m\geqslant 2$, and derive estimates on the growth rates of the evolved graphs, based on a new version of the maximum principle for properly immersed submanifolds that extends the well‐known maximum principle of Ecker ...
Andreas Savas Halilaj, Knut Smoczyk
wiley   +1 more source

Existence of stable periodic solutions for quasilinear parabolic problems in the presence of well-ordered lower and upper-solutions

Electronic Journal of Differential Equations, 2002
We present existence and stability results for periodic solutions of quasilinear parabolic equation related to Leray-Lions's type operators. To prove existence and localization, we use the penalty method; while for stability we use an approximation ...
Abderrahmane El Hachimi, Abdelilah Lamrani Alaoui   +1 more
doaj  

Blow-Up Analysis for a Quasilinear Degenerate Parabolic Equation with Strongly Nonlinear Source

Abstract and Applied Analysis, 2012
We investigate the blow-up properties of the positive solution of the Cauchy problem for a quasilinear degenerate parabolic equation with strongly nonlinear source ut=div(|∇um|p−2∇ul)+uq,  (x,t)∈RN×(0,T), where N≥1, p>2 , and m, l,  q>1, and give a ...
Pan Zheng, Chunlai Mu, Dengming Liu, Xianzhong Yao, Shouming Zhou   +4 more
doaj   +1 more source

ON THE GLOBAL EXISTENCE OF SOLUTIONS TO QUASILINEAR PARABOLIC EQUATIONS [PDF]

Glasgow Mathematical Journal, 2004
The subject of the paper is the following quasilinear parabolic problem (P): \[ u_t - \text{div\,} (a(t,x,u) \nabla u) = f(t,x,u, \nabla u) \qquad \text{for} \quad t>0, \; x \in \Omega, \] \[ u(t,x) = 0 \quad \text{for} \quad t>0, \; x \in \partial \Omega, \qquad u(0,x) = \varphi (x) \quad \text{for} \quad x \in \bar \Omega.
openaire   +1 more source

Understanding Coherent Turbulence and the Roll‐Cell Transition With Lagrangian Coherent Structures and Frame‐Indifferent Fluxes

Journal of Geophysical Research: Atmospheres, Volume 129, Issue 18, 28 September 2024.
Abstract We present the first analysis of frame‐indifferent (objective) fluxes and material vortices in Large Eddy Simulations of atmospheric boundary layer turbulence. We extract rotating fluid features that maintain structural coherence over time for near‐neutral, transitional, and convective boundary layers.
Nikolas Aksamit, Marwan Katurji, Jiawei Zhang   +2 more
wiley   +1 more source

Maximum principle for the weak solutions of the Cauchy problem for the fourth‐order hyperbolic equations

Proceedings in Applied Mathematics and Mechanics, Volume 24, Issue 1, June 2024.
Abstract We investigate the maximum principle for the weak solutions to the Cauchy problem for the hyperbolic fourth‐order linear equations with constant complex coefficients in the plane bounded domain.
Kateryna Buryachenko
wiley   +1 more source

Existence and uniqueness for a coupled parabolic‐hyperbolic model of MEMS

Mathematical Methods in the Applied Sciences, Volume 47, Issue 7, Page 6310-6353, 15 May 2024.
Local wellposedness for a nonlinear parabolic‐hyperbolic coupled system modeling Micro‐Electro‐Mechanical System (MEMS) is studied. The particular device considered is a simple capacitor with two closely separated plates, one of which has motion modeled by a semilinear hyperbolic equation.
Heiko Gimperlein, Runan He, Andrew A. Lacey   +2 more
wiley   +1 more source