Sentence examples for in time solution from inspiring English sources

This evolution equation falls into a class of quasi-linear parabolic systems which allow unique, local in time solution in certain Lebesgue spaces.

Pukach et al. [9] studied sufficient conditions of nonexistence of global in time solution for a nonlinear evolution equation with memory generalizing the Voigt Kelvin model.

As for problem (1.2), it is well known that problem (1.2) has a classical, maximal in time solution and that the comparison principle is true (using the methods of [3]).

Following a similar method to Theorems 3 and 4 on p.967 in [3] for Navier-Stokes equations, then there exists a globally in time solution ((u(x), d(x))in Etimes E) to (1.1) that satisfies (1.5).

Irrespective of energy positivity, there is a unique local-in-time solution for arbitrary finite-energy Goursat datum, for all n ⩾ 3, establishing evolution from the given lightcone to any sufficiently close lightcone.

In general, it is difficult to directly show the existence of a unique global-in-time solution to (1.2 - 1.4 1.2 - 1.4

When (tau=0), for the model (1.1) with logistic source, in [6] it is shown that under some suitable assumptions, then there exist initial data such that the smooth local-in-time solution of a higher-dimensional chemotaxis system blows up in finite time.

The emphasis of the work is on third order in space and second order in time solutions (in both single and double precision).

I am convinced that, in time, solutions can be found and a Canada-style deal can be made to work for our constituents' jobs and living standards, for the Europeans and for MPs.

The aim of this work is to study the asymptotic behaviour of global in time solutions of the Vlasov Poisson Fokker Planck system in three dimensions.

We also find a threshold for the existence of global in time solutions of the evolution equation for the MEMS in the form of either a heat or a damped wave equation.