Sentence examples for mild solution with from inspiring English sources

(H40) The IVP (6.1) has a lower mild solution and an upper mild solution with.

(H37) The IVP (3.1) and (3.2) has a lower mild solution and an upper mild solution with.

(H36) is order-preserving, that is, whenever (H37) The IVP (3.1) and (3.2) has a lower mild solution and an upper mild solution with.

(H39) is order-preserving, that is, whenever (H40) The IVP (6.1) has a lower mild solution and an upper mild solution with.

If (t_{max}mild solution with (U_{0}in D mathcal{A})).

By using Theorem 6.1.5 in Pazy [19] (see also [20]), we know that any mild solutions with initial data in (D mathcal {A})) are strong.

We consider the Keller Segel system coupled with the Navier Stokes fluid in the whole space, and prove the existence of global mild solutions with the small initial data in the scaling invariant space.

Combining the techniques of fractional calculus, measure of noncompactness, and fixed point theorem with respect to a k-set-contractive operator, we obtain a new result on the existence of mild solutions with the assumption that the nonlinear term satisfies some growth condition and noncompactness measure condition.

Then IVP (3.1) and (3.2) has at least one mild solution on with.

Moreover, exponential stability of the mild solution is established with sufficient conditions.

Let and such that then there exists a mild solution of (5.1) with.