Sentence examples for under which solutions from inspiring English sources

Hawking, along with his colleague Roger Penrose, clarified the conditions under which solutions to Einstein's equations must devolve into a "singularity," quite literally a point of no return.

We give conditions under which solutions x to the slow equations converge weakly to an Itô diffusion X as ε→0.

Then, we consider the long-time behavior of the solutions of system (1.2) and derive precise conditions under which the solutions converge exponentially to a unique constant steady-state solution.

These solutions show nicely the variation of all different terms in the entropy transport equation and highlight also restrictions under which such solutions can be obtained.

The conditions under which degenerate solutions are possible are also identified.

Further research should focus on the context conditions under which multiple solutions are effective.

We have also provided conditions under which the solutions to (11) and (14) coincide.

In particular, we give conditions on data functions under which stationary solutions exist.

We also give sufficient conditions under which all solutions are asymptotically polynomial.

However, entry conditions under which these solutions can occur are not known.

In the following theorem we get conditions under which the solutions of a nabla fractional equation tend to zero.