Sentence examples for with the initial data from inspiring English sources

with the initial data.

with the initial data (52).

with the initial data in (1.2).

Step three: the continuity of solution with the initial data.

We supplement equation (1.1) with the initial data.

To see this, pick t sufficiently small so that α ( t ) agrees with the initial data.

We now consider equation (5) with the initial data (u x,0)=varphi(x)=0).

associated with the initial data u ( 0, x ) = u 0, b ( 0, x ) = b 0. (4).

where the dual sequence is defined by a similar relationship as with the initial data.

To prove (S(t+s)=S t S s)), we define the solutions (u(t)) associated with the initial data (u_{0}) and (v(t)) associated with the initial data (u(s)).

Let in (4.35), by (4.34) we get that is the solution of (2.8) and (2.9) with the initial data.