Sentence examples for boundary value problems initial from inspiring English sources

Then the desired stochastic representations are obtained for boundary value problems, initial boundary value problems, and the initial value problems, respectively.

In this paper, we deal with the boundary value problems without initial condition for Schrödinger systems in cylinders.

There have also been many profound results on the existence of global solutions and asymptotic behavior of the solutions for the initial boundary value problems and the initial value problems of fourth order nonlinear pseudo-parabolic equations.

The method has been applied to initial boundary value problems [4 9], fractal initial value problems [10, 11], q-difference equations [12] and fuzzy equations [13 15], etc.

One could generically classify these problems into two types; boundary value problems with nonlocal initial conditions, and boundary value problems with nonlocal boundary conditions.

Solvability conditions for boundary value problems with weighted initial conditions are established in [23 33].

Moreover, many valuable results related to boundary value problems (BVPs) or initial problems for fractional differential equations have been achieved by some scholars (see [5 11]).

Moreover, shear wave solutions are found in [3], where some explicit examples of blow-up for boundary value problems with smooth initial data are shown.

We restrict our consideration to two cases: the initial boundary value problems of (1.1) and the initial value problems of (1.1).

The boundary value problem without initial condition for parabolic equation was investigated in [3].

In [7], we studied the boundary value problem without initial condition for Schrödinger systems in domain with conical points.