scholarly journals Planar Waves of the Buffered Bistable System

2013 ◽  
Vol 2013 ◽  
pp. 1-13
Author(s):  
Xiaohuan Wang ◽  
Guangying Lv
Keyword(s):  
Large Time ◽  
Mean Curvature Flow ◽  
Large Time Behavior ◽  
Bistable System ◽  
Time Behavior ◽  
Almost Periodic ◽  
Drift Term ◽  
Planar Front ◽  
Special Cases ◽  
The Mean

This paper is concerned with the large time behavior of disturbed planar fronts in the buffered bistable system inℝn(n≥2). We first show that the large time behavior of the disturbed fronts can be approximated by that of the mean curvature flow with a drift term for all large time up tot=+∞. And then we prove that the planar front is asymptotically stable inL∞(ℝn)under ergodic perturbations, which include quasiperiodic and almost periodic ones as special cases.

scholarly journals Existence of martingale solutions and large-time behavior for a stochastic mean curvature flow of graphs

2020 ◽  
Author(s):  
Nils Dabrock ◽  
Martina Hofmanová ◽  
Matthias Röger
Keyword(s):  
Mean Curvature ◽  
Large Time ◽  
Mean Curvature Flow ◽  
Stochastic Perturbation ◽  
Curvature Flow ◽  
Large Time Behavior ◽  
Time Behavior ◽  
Viscosity Sense ◽  
Stochastic Mean Curvature Flow ◽  
Martingale Solutions

Abstract We are concerned with a stochastic mean curvature flow of graphs over a periodic domain of any space dimension. For the first time, we are able to construct martingale solutions which satisfy the equation pointwise and not only in a generalized (distributional or viscosity) sense. Moreover, we study their large-time behavior. Our analysis is based on a viscous approximation and new global bounds, namely, an $$L^{\infty }_{\omega ,x,t}$$ L ω , x , t ∞ estimate for the gradient and an $$L^{2}_{\omega ,x,t}$$ L ω , x , t 2 bound for the Hessian. The proof makes essential use of the delicate interplay between the deterministic mean curvature part and the stochastic perturbation, which permits to show that certain gradient-dependent energies are supermartingales. Our energy bounds in particular imply that solutions become asymptotically spatially homogeneous and approach a Brownian motion perturbed by a random constant.

scholarly journals Global well-posedness of the full compressible Hall-MHD equations

2021 ◽  
Vol 10 (1) ◽  
pp. 1235-1254
Author(s):  
Qiang Tao ◽  
Canze Zhu
Keyword(s):  
Global Solution ◽  
Large Time ◽  
Initial Temperature ◽  
Large Time Behavior ◽  
Initial Energy ◽  
Mhd Equations ◽  
Well Posedness ◽  
Time Behavior ◽  
Magnetohydrodynamic Flows ◽  
Hall Mhd

Abstract This paper deals with a Cauchy problem of the full compressible Hall-magnetohydrodynamic flows. We establish the existence and uniqueness of global solution, provided that the initial energy is suitably small but the initial temperature allows large oscillations. In addition, the large time behavior of the global solution is obtained.

Large Time Behavior of Solutions to One Nonlinear Integro-Differential Equation

2008 ◽  
Vol 15 (3) ◽  
pp. 531-539
Author(s):  
Temur Jangveladze ◽  
Zurab Kiguradze
Keyword(s):  
Magnetic Field ◽  
Differential Equation ◽  
Boundary Conditions ◽  
Large Time ◽  
Dirichlet Boundary ◽  
Large Time Behavior ◽  
Dirichlet Boundary Conditions ◽  
Time Behavior ◽  
Integro Differential Equation ◽  
Homogeneous Data

Abstract Large time behavior of solutions to the nonlinear integro-differential equation associated with the penetration of a magnetic field into a substance is studied. The rate of convergence is given, too. Dirichlet boundary conditions with homogeneous data are considered.

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