Results 51 to 60 of about 1,241 (227)

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

Remarks on global solutions to the initial-boundary value problem for quasilinear degenerate parabolic equations with a nonlinear source term [PDF]

Opuscula Mathematica, 2019
We give an existence theorem of global solution to the initial-boundary value problem for \(u_{t}-\operatorname{div}\{\sigma(|\nabla u|^2)\nabla u\}=f(u)\) under some smallness conditions on the initial data, where \(\sigma (v^2)\) is a positive ...
Mitsuhiro Nakao
doaj   +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

Expanding solutions of quasilinear parabolic equations

Communications on Pure and Applied Analysis, 2021
By using the theory of maximal $L^{q}$-regularity and methods of singular analysis, we show a Taylor's type expansion--with respect to the geodesic distance around an arbitrary point--for solutions of quasilinear parabolic equations on closed manifolds. The powers of the expansion are determined explicitly by the local geometry, whose reflection to the
openaire   +4 more sources

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

A duality for prescribed mean curvature graphs in Riemannian and Lorentzian Killing submersions

Mathematische Nachrichten, Volume 297, Issue 5, Page 1581-1600, May 2024.
Abstract We develop a conformal duality for space‐like graphs in Riemannian and Lorentzian three‐manifolds that admit a Riemannian submersion over a Riemannian surface whose fibers are the integral curves of a Killing vector field, which is time‐like in the Lorentzian case.
Andrea Del Prete, Hojoo Lee, José Miguel Manzano   +2 more
wiley   +1 more source

The Mullins–Sekerka problem via the method of potentials

Mathematische Nachrichten, Volume 297, Issue 5, Page 1960-1977, May 2024.
Abstract It is shown that the two‐dimensional Mullins–Sekerka problem is well‐posed in all subcritical Sobolev spaces Hr(R)$H^r({\mathbb {R}})$ with r∈(3/2,2)$r\in (3/2,2)$. This is the first result, where this issue is established in an unbounded geometry.
Joachim Escher, Anca‐Voichita Matioc, Bogdan‐Vasile Matioc   +2 more
wiley   +1 more source

A multiplicity result for a class of quasilinear elliptic and parabolic problems

Electronic Journal of Differential Equations, 1997
We prove the existence of infinitely many solutions for a class of quasilinear elliptic and parabolic equations, subject respectively to Dirichlet and Dirichlet-periodic boundary conditions.
M. R. Grossinho, Pierpaolo Omari
doaj  

Directed mean curvature flow in noisy environment

Communications on Pure and Applied Mathematics, Volume 77, Issue 3, Page 1850-1939, March 2024.
Abstract We consider the directed mean curvature flow on the plane in a weak Gaussian random environment. We prove that, when started from a sufficiently flat initial condition, a rescaled and recentred solution converges to the Cole–Hopf solution of the KPZ equation.
Andris Gerasimovičs, Martin Hairer, Konstantin Matetski   +2 more
wiley   +1 more source