of a first-order partial differential equation
of continuously-differentiable functions in an interval , satisfying the equations
where the multiplication of the vectors is the scalar product, and where
is a non-linear first-order partial differential equation in the unknown function . Here , , , , .
The importance of a characteristic strip consists in the fact that it is used in the study of, and in the search for, solutions of equation (*).
See also Characteristic.
|||E. Kamke, "Differentialgleichungen: Lösungen und Lösungsmethoden" , 2. Partielle Differentialgleichungen erster Ordnung für die gesuchte Funktion , Akad. Verlagsgesell. (1944)|
|||P. Hartman, "Ordinary differential equations" , Birkhäuser (1982)|
A characteristic strip is sometimes called a bicharacteristic.
In the modern theory, the characteristic strips of a partial differential equation carry the wave front sets of solutions of a partial differential equation.
|[a1]||R. Courant, D. Hilbert, "Methods of mathematical physics. Partial differential equations" , 2 , Interscience (1962) (Translated from German)|
|[a2]||L.V. Hörmander, "The analysis of linear partial differential operators" , 1 , Springer (1983)|
Characteristic strip. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Characteristic_strip&oldid=16803