Definition
A partial differential equation is hyperbolic at a point P provided that the Cauchy problem is uniquely solvable in a neighborhood of P for any initial data given on a non-characteristic hypersurface passing through P. Here the prescribed initial data consists of all (transverse) derivatives of the function on the surface up to one less than the order of the differential equation.
Read more about this topic: Hyperbolic Partial Differential Equations
Famous quotes containing the word definition:
“One definition of man is “an intelligence served by organs.””
—Ralph Waldo Emerson (1803–1882)
“... if, as women, we accept a philosophy of history that asserts that women are by definition assimilated into the male universal, that we can understand our past through a male lens—if we are unaware that women even have a history—we live our lives similarly unanchored, drifting in response to a veering wind of myth and bias.”
—Adrienne Rich (b. 1929)
“It is very hard to give a just definition of love. The most we can say of it is this: that in the soul, it is a desire to rule; in the spirit, it is a sympathy; and in the body, it is but a hidden and subtle desire to possess—after many mysteries—what one loves.”
—François, Duc De La Rochefoucauld (1613–1680)