Sentence examples for long time existence from inspiring English sources

In this note, we study the long time existence of the Calabi flow on X= Cn/Zn+iZn.

We consider a fully nonlinear parabolic equation with nonlinear Neumann type boundary condition, and show the long time existence and convergence of the flow.

We prove a long time existence, of order C r)ε−r for all r⩾3, for small solutions, of order ε≪1, in high Sobolev norms of Klein Gordon equation with Hamiltonian nonlinearities.

In this paper, we investigate the long time existence and uniqueness of small solution to d, for d= 2,3, dimensional Prandtl system with small initial data which is analytic in the horizontal variables.

In this paper, we are going to show the long time existence of the smooth solution for the porous medium equations in a smooth bounded domain:(0.1){ut="△umin Ω×[0,∞),u x,0)="u0>0in Ω,u x,t)= 0for x∈∂Ω where m>1 is the permeability.

We outline how the structure stability results, the stability of the Schauder estimates and of the Harnack inequalities can be used to prove regularity and long time existence theorems for solutions of the subRiemannian mean curvature flow and the total curvature flow of graphs over bounded sets in step 2 Carnot groups and even in some non-nilpotent Lie groups.

As an application, we also explain how to apply this inequality in order to establish a long-time existence result for a class of nonlinear parabolic problems.

Careful evaluation of the patient's history with the relatively long time for existence of the nodule and the subtle clinical findings, in association with the specific frozen section histology findings and imaging features, are essential for intra-operative decision making to avoid unnecessary sacrifice of the parent nerve.

In addition to the long time established existence of apoptosis, autophagy has been increasingly described in eukaryotic cells [39].

As we all know, products take a long time to come into existence from beginning to end — especially at Apple.

Motivated by the persistence of the global attractor under a white noise, in our paper, we will investigate the long time behavior and the existence of the global random attractor of stochastic viscous coupled Camassa-Holm equation: m t − ε m x x = 2 m u x + m x u + ( m v ) x + n v x + h W t, m = u − u x x, n t − ε n x x = 2 n v x + n x v + ( n u ) x + m u x, n = v − v x x, (1.5).