Results 81 to 90 of about 12,485 (201)

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

Global existence, uniqueness, and continuous dependence for a reaction-diffusion equation with memory

Electronic Journal of Differential Equations, 1996
initial data are established for a quasilinear functional reaction-diffusion equation which arises from a two-dimensional energy balance climate model.
Georg Hetzer
doaj  

The applications of Sobolev inequalities in proving the existence of solution of the quasilinear parabolic equation

Boundary Value Problems, 2020
The aim of this paper is to show some applications of Sobolev inequalities in partial differential equations. With the aid of some well-known inequalities, we derive the existence of global solution for the quasilinear parabolic equations.
Yuanfei Li, Lianhong Guo, Peng Zeng
doaj   +1 more source

Locally Invariant Manifolds for Quasilinear Parabolic Equations

Rocky Mountain Journal of Mathematics, 1991
The paper is concerned with the geometric study of an evolution equation of the form \(x'-Lx=f(t,\lambda,x)\), where \(L:D(L)\to X\) is the generator of a holomorphic semigroup and the nonlinearity \(f\) acts essentially from some interpolation space \(D_ L(\theta+1)\) to \(D_ L(\theta)\).
openaire   +2 more sources

Quasilinear parabolic equations with localized reaction

Advances in Differential Equations, 2005
In this paper, we study a nonnegative blow-up solution of the Dirichlet problem for a quasilinear parabolic equation $(u^{\alpha})_t=\Delta u +f(u) + g(u(x_0(t),t))$ in $B(R)$, where $B(R)=\{ x \in \mathbf{R^N}\,;\, |x| < R\}$, $0 < \alpha \le 1$, $x_0(t)\in C^{\infty}([0,\infty) ;B(R))$ satisfies $x_0(t)\not = 0$, and $f(\xi)$ and $g(\xi)$ satisfy ...
Fukuda, Isamu, Suzuki, Ryuichi
openaire   +2 more sources

Sturm attractors for quasilinear parabolic equations [PDF]

Journal of Differential Equations, 2018
21 pages, 1 ...
openaire   +2 more sources

Development of attenuation and diffraction corrections for linear and nonlinear Rayleigh surface waves radiating from a uniform line source

AIP Advances, 2016
In recent studies with nonlinear Rayleigh surface waves, harmonic generation measurements have been successfully employed to characterize material damage and microstructural changes, and found to be sensitive to early stages of damage process.
Hyunjo Jeong, Shuzeng Zhang, Sungjong Cho, Xiongbing Li   +3 more
doaj   +1 more source

High precision compact numerical approximation in exponential form for the system of 2D quasilinear elliptic BVPs on a discrete irrational region. [PDF]

MethodsX, 2022
Mohanty RK, Setia N, Khurana G, Manchanda G.   +3 more
europepmc   +1 more source

On nonlocal quasilinear equations and their local limits

, 2016
We introduce a new class of quasilinear nonlocal operators and study equations involving these operators. The operators are degenerate elliptic and may have arbitrary growth in the gradient.
Chasseigne, Emmanuel, Jakobsen, Espen
core   +1 more source

Nonlinear multidimensional parabolic-hyperbolic equations

Electronic Journal of Differential Equations, 2007
This paper deals with the coupling of a quasilinear parabolic problem with a first order hyperbolic one in a multidimensional bounded domain $Omega$. In a region $Omega_{p}$ a diffusion-advection-reaction type equation is set while in the complementary ...
loria Aguilar, Laurent Levi, Monique Madaune-Tort   +2 more
doaj