Sentence examples for a strong solution to from inspiring English sources

We establish the existence and uniqueness of a strong solution to the Cauchy problem for a singular diffusion equation with random noise in Rd with initial data in L2 Rd) with bounded variation or in H1 Rd).

"We hadn't even asked ourselves if there will be a stigma attached to this, because we are so sure it is a strong solution to a climate problem," said Jeff Seabright, vice president for environment and water resources at Coca-Cola.

Hence, the mild solution (x t)) is a strong solution to problem (3.1).

(1.1) hold almost everywhere in (mathbb{R}times 0,T)), then ((rho,u)) is called a strong solution to (1.1).

In the following, we prove that a mild solution can become a strong solution to problem (3.1) under some assumptions.

The condition C1 ensures the existence and uniqueness of a strong solution to model (1), see [31] for details.

Let ( ρ, u, d ) be a local strong solution to the problem (1.1 - 1.6 1.1 - 1.6

Obviously, under the above assumptions, there exists a unique strong solution to (1) (see, e.g., [14]).

We prove the global existence of a unique strong solution to the initial boundary value problem for the 3-D chemotaxis model on a bounded domain with slip boundary condition when the initial perturbation is small in (H^{2}).

In Section 2, the main results about the existence and dynamical behaviors of a global strong solution to FBVP with two different initial data for compressible Navier-Stokes equations are stated.

If the initial density ρ0 is bounded away from zero, then we can apply standard arguments to prove the global existence of a unique strong solution to the initial boundary value problem (2 -(4) and (8), since the system can be uncoupled into a linear transport equation and two linear parabolic equations.