Sentence examples for for nonlinear terms from inspiring English sources

In this manuscript no restrictive assumptions are taken for nonlinear terms.

Therefore, it is naturally to impose special monotonous conditions for nonlinear terms.

In order to deal with our main results, we need the following assumptions for nonlinear terms f and g.

It is noted that discretized model (3.1) can be considered as using the standard Euler method for the first derivative and a nonlocal expression for nonlinear terms.

However, compared with the Navier-Stokes equations, the additional difficulty here is that some more explicit estimates for nonlinear terms should be done.

In the previous related results on boundary value problems for p-Laplacian differential equations by means of the monotone iterative method, the monotone-type conditions for nonlinear terms f with respect to the functions u or their derivatives are usually required.

For nonlinear term f, the sublinear and superlinear cases were considered in [20].

Using the Faedo-Galerkin method and the linearization method for nonlinear term, the existence and uniqueness of a weak solution are proved.

By combining the L p -integral norm estimate method and the technique of differential inequalities, we find that the critical exponent of extinction for the non-negative weak solution is determined by the competition of nonlinear terms for 1 < p < 2, and decay estimates depend on the choices of initial data, coefficients, and domain.

The temporal terms are treated by the Euler implicit/explicit scheme, which is implicit for the linear terms and explicit for the nonlinear terms.

In view of the advantages of the explicit scheme for the nonlinear terms, we adopt the implicit/explicit scheme for the Boussinesq equations (1.1).