Sentence examples for small solutions of from inspiring English sources

We study the long-time behavior of small solutions of the initial-value problem for a generalized Boussinesq equation.

Chen and Price [15] obtained the (L^{2}) time decay rate for small solutions of the 3D micropolar equations via Kato's method.

We prove a long time existence, of order C r)ε−r for all r⩾3, for small solutions, of order ε≪1, in high Sobolev norms of Klein Gordon equation with Hamiltonian nonlinearities.

We study the long-time behavior of small solutions of the initial-value problem for the generalized Korteweg-de Vries equation ∂tu + ∂x3u + ∂xF u) = 0 (gKdV) u x, 0) = g(x).

We obtain a lower bound for the degrees of nonlinearity of the perturbation which guarantees that the small solutions of the nonlinear problem behave asymptotically like the solutions of the associated linear problem.

We obtain a lower bound for the degrees of nonlinearity which allows us to establish a nonlinear scattering result for small perturbations; that is, the small solutions of the nonlinear problem behave asymptotically like the solution of the associated linear problem.

Mix a small solution of ammonia and water together and sponge it all over the appliance.

There are smaller solutions, of course, but this is the biggest standalone monitor I've seen that just runs off USB.

Thus G 1 6 x - is the smallest solution of (6.10).

By analogous reasoning, one shows the existence of the smallest solution of (5.1).

The existence of the smallest solution of (1.1) in can be proven in a similar way.