Sentence examples for growth of the solution from inspiring English sources

For this, we carefully design a function space which captures the growth of the solution in a weighted Sobolev norm, and show that the ellipsoidal relaxation operator is Lipschitz continuous in the induced metric.

By using intrinsic scaling, the exact growth of the solution near the free boundary is established.

While in Theorem 3.4, the function f is the main factor to suppress growth of the solution in condition (H4).

In these results above, the condition (H3) or (H3′) plays an important role to suppress growth of the solution.

It shows that growth of the solution x ( t ) is so slow that it is near to be bound.

References [1, 17] reveal that the noise plays an important role to suppress the growth of the solution.

Hence, here we just study the order of the growth of the solutions.

then, the estimation was used to study the boundedness, asymptotic behavior, slowly growth of the solutions of the integral equation (1.7).

From Theorem 1.10, we further study the growth of the solutions of a class of q-difference differential equation and obtain a result as follows.

In this paper, we estimate the order of growth of the solutions of the equation f ( k z ) = k f ( z ) f ′ ( z ) and investigate the periodicity of the solutions in the case k = 3, which give an answer to the question proposed by Beardon (Comput. Methods Funct. Theory 12(1):20122012 2012).

Integrability is not conditioned by the local singularity behaviour which explains why the singularity confinement test is not sufficient and one must consider the growth properties of the solution.