Other Kinds of Weak Solution
The notion of weak solution based on distributions is sometimes inadequate. In the case of hyperbolic systems, the notion of weak solution based on distributions does not guarantee uniqueness, and it is necessary to supplement it with entropy conditions or some other selection criterion. In fully nonlinear PDE such as the Hamilton-Jacobi equation, there is a very different definition of weak solution called viscosity solution.
Read more about this topic: Weak Solution
Famous quotes containing the words kinds, weak and/or solution:
“In fact, words are well adapted for description and the arousing of emotion, but for many kinds of precise thought other symbols are much better.”
—J.B.S. (John Burdon Sanderson)
“Why, therefore, should we do ourselves this wrong,
Or others—that we are not always strong—
That we are sometimes overborne with care—
That we should ever weak or heartless be,
Anxious or troubled—when with us is prayer,
And joy and strength and courage are with Thee?”
—Richard Chenevix Trench (1807–1886)
“Who shall forbid a wise skepticism, seeing that there is no practical question on which any thing more than an approximate solution can be had? Is not marriage an open question, when it is alleged, from the beginning of the world, that such as are in the institution wish to get out, and such as are out wish to get in?”
—Ralph Waldo Emerson (1803–1882)