Sentence examples for established solutions for from inspiring English sources

where ξ = c t + k 1 x 1 + k 2 x 2 + l 1 y 1 + l 2 y 2 + ξ 0. Remark 3 As one can see, the established solutions for the space-time fractional Fokas equation above are different from the results in [30] and are new exact solutions so far to our best knowledge.

That not only means those established outfits have an established solution for creating Wii U games; it also means Unity's 1.2 million existing customers - scores of them indies and students - already own a familiar tool that can now let them build games for the new console.

We carried out a system comparison in order to structure the problem and to identify the established solution approaches for the organization of cloud ecosystems.

As a benchmark for our results we use the well established analytical solutions for regular, periodic honeycombs of Gibson and Ashby (1999).

Then in Section 4 we apply this method to establish exact solutions for the space-time fractional Fokas equation, the space-time fractional ( 2 + 1 ) -dimensional dispersive long wave equations and the space-time fractional fifth-order Sawada-Kotera equation.

By a standard density argument, it is known that the same result can be established for strong solutions and for almost every t.

In their papers, they established the entire solutions for Fisher-KPP equation in one- and high-dimensional spaces by combining traveling fronts with different speeds.

Finally, a relationship between the problem considered here with another non-classical problem for the heat equation is established, and explicit solutions for this second problem are also obtained.

We end this section by giving the mayor tools to establish existence of solutions for (DVEP).

In this letter, we establish some exact solutions for complex nonlinear Klein Gordon equation.

In this article, we establish the exact solutions for the combined KdV-mKdV and Gardner-KP equations.