Sentence examples for prove the regularity from inspiring English sources

In the next step we are going to prove the regularity of solutions of problem (1.1) belonging to the order intervals and, respectively.

For linearized problem we prove the regularity of the solution in the random space and consequently the spectral accuracy of the gPC-SG method.

In Section 3, we prove the regularity for the solutions of the exterior problem (1.1) and give the estimate for the regularity of solutions.

The main aim of this paper is to prove the regularity of solutions in the subspace H + i of (H i [0, 1] 7(i = 2, 4) for systems (1.1 - 1.7 1.1 - 1.7

The first step is to construct the approximating solution sequence; in the second step, we prove the regularity of the solution we have obtained; and in the last step, we prove the uniqueness.

In order to prove the regularity of the mild solution, we use the further assumptions, it is easy to conclude that the function ω(t) is also uniformly Hölder continuous in t ∈ J. Consider the following fractional differential equation (3.1).

Later on, Qin et al. [8, 9] proved the regularity of weak solutions and existence of classical solution.

Section 3 is devoted to proving the regularity of the mild solution for infinite horizon stochastic delay evolution equation.

In the following we give a type of the Burkholder-Davis-Gundy inequality which will play an important role in proving the regularity property of the mild solution of (2.1).

Indeed, they proved the regularity of weak solutions of the MHD equations (1.1) if the velocity field satisfies the Serrin condition in critical Lebesgue spaces, begin{aligned} uin L^{p}bigl 0,T L^{q}bigl(mathbf{R}^{3} bigr bigr) quadmbox{for } frac{2}{p} + frac{3}{q}leq1, 3< qleq infty.

Now we will prove the global regularity of the solution.