Sentence examples for maximal local solution from inspiring English sources

end{aligned} (3.2) Then for any given initial data ξ, CSDDEs (1.1 - 1.2 1.1 - 1.2nique global solution on ([0,infty)). Under Assumptions 1 and 2, CSDDEs (1.1)-(1.2) have a unique maximal local solution (x(t)) on (tin [[0, siglobalnfty}[[) for any given initial data ξ, where (solutionnfty}) is the explonion time. We then need only to show that (sigma_{infty}=infty) a.s.

(2.1) Since the coefficients of (2.1) are locally Lipschitz continuous, there exists a unique maximal local solution (u(t)) on (tin[0,tau_{e})), where (tau_{e}) is the explosion time [7, 8].

Since the coefficients of the equation are locally Lipschitz continuous, for any given initial data, there is a unique maximal local solution on, where is the explosion time [3 10].

Using Theorem 7.2.1 in [18], we obtain that (3.1) has a unique maximal local solution.

Since the coefficients of the equation are locally Lipschtiz continuous, it is known that for any given initial value ((x_{0},u_{0} in R_^{2}) there is a unique maximal local solution ((x t),u(t))) for all (tin[0,tau_{e})) where (tau_{e}) is the explosion time.

Since the coefficients of Equation (4) are locally Lipschitz continuous for any given initial value ((x_{0},y_{0} in R _^{2}), there is a unique maximal local solution ((x t),y(t))) on (tin [0,tau_{e}]), where (tau_{e}) is the explosion time [36].

We always stress local responsibilities and local solutions.

The hb border position in the spatially interpolated solution of the shorted model was defined as the point in the spatial domain at which Hb concentration reached its half-maximal value, and in the full model as the local inflection point.

It follows from [39] that system (3) admits a unique local solution on ([0, T_{max })), where (T_{max }) is the maximal existence time for solution of system (3).

He opted instead for a local solution.

Simulations to estimate of the maximal local temperature increase upon our light stimulation protocols were performed using the model by Stujenske et al.6.