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:
“There are two kinds of men, and only two, and that young man is one kind. He is high-minded, he is pure, he’s the kind of man that the world pretends to look up to, and in fact despises. He is
the kind of man who breeds unhappiness, particularly in women.”
—Robert Bolt (1924–1995)
“Learning is, in too many cases, but a foil to common sense; a substitute for true knowledge. Books are less often made use of as “spectacles” to look at nature with, than as blinds to keep out its strong light and shifting scenery from weak eyes and indolent dispositions.... The learned are mere literary drudges.”
—William Hazlitt (1778–1830)
“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)