Books > Science & Mathematics > Physics > Classical mechanics
|
Buy Now
Justification of the Courant-Friedrichs Conjecture for the Problem About Flow Around a Wedge (Hardcover)
Loot Price: R3,197
Discovery Miles 31 970
|
|
Justification of the Courant-Friedrichs Conjecture for the Problem About Flow Around a Wedge (Hardcover)
Expected to ship within 12 - 17 working days
|
The classical problem about a steady-state supersonic flow of an
inviscid non-heat-conductive gas around an infinite plane wedge
under the assumption that the angle at the vertex of the wedge is
less than some limit value is considered. The gas is supposed to be
in the state of thermodynamical equilibrium and admits the
existence of a state equation. As is well-known, the problem has
two discontinuous solutions, one of which is associated with a
strong shock wave (the gas velocity behind the shock wave is less
than the sound speed) and the second one corresponds to the weak
shock wave (the gas velocity behind the shock wave is, in general,
larger than the sound speed) (Courant R, Friedrichs K.O. Supersonic
flow and shock waves. N. Y.: Interscience Publ. Inc., 1948). One of
the possible explanations of this phenomenon was given by Courant
and Friedrichs. They conjectured that the solution corresponding to
the strong shock wave is instable in the sense of Lyapunov, whereas
the solution corresponding to the weak shock wave is stable. This
conjecture has been confirmed in a number of studies in which
either particular cases were considered or the proposed
argumentation was given at the qualitative (mostly, physical) level
of rigor. In this monograph, the Courant-Friedrichs conjecture is
strictly mathematically justified at the linear level. The
mechanism of generating the instability for the case of a strong
shock is explained. The smoothness of the solution essentially
depends on the peculiarity of the boundary at the vertex of the
wedge. The situation with a weak shock drastically differs from the
previous one. It is amazing but for the compactly supported initial
data the solution to the linear problem reaches the steady state
regime infinite time.
General
Is the information for this product incomplete, wrong or inappropriate?
Let us know about it.
Does this product have an incorrect or missing image?
Send us a new image.
Is this product missing categories?
Add more categories.
Review This Product
No reviews yet - be the first to create one!
|
|
Email address subscribed successfully.
A activation email has been sent to you.
Please click the link in that email to activate your subscription.