The phrase "a long time existence" is not correct in standard written English.
It is awkward and does not convey a clear meaning. A more appropriate phrase would be "a long existence" or "long-term existence."
Example: "The ancient tree has had a long existence, surviving through many seasons and storms."
Alternatives: "a lengthy existence" or "an extended existence."
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.
We consider a fully nonlinear parabolic equation with nonlinear Neumann type boundary condition, and show the long time existence and convergence of the flow.
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 we all know, products take a long time to come into existence from beginning to end — especially at Apple.
The unusual "mirror image" graphics for the campaign, Mr. Newman said, stemmed from creative executives at Bates USA noticing "that the back of the Kool pack has some great copy about the brand's being in existence a long time and its premium quality".
Very few cities in the world have such a long time of uninterrupted and organized existence like Dhaka as a historic city.
Said Abu Shakra, director of the town's well-known art gallery, and a long time promoter of co-existence between Jews and Arabs, said he now felt "depressed and frustrated" in the face of the ascendancy of Mr Lieberman, who once proposed the bombing of Egypt's Aswan Dam and suggested that Arab Knesset members who had talks with Hamas representatives should be executed.
