Riemann Problem for First-Order Partial Equations Without the Convexity of a State Functions
Küçük Resim Yok
Tarih
2015
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Springer-Verlag Berlin
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
In this work, the exact solution of the Riemann problem for first-order nonlinear partial equation with non-convex state function in Q(T) = {(x, t)vertical bar x is an element of I = (-infinity, infinity), t is an element of [0, T)} subset of R-2 is found. Here F is an element of C-2 (Q(T)) and F '' (u) change their signs, that is F(u) has convex and concave parts. In particular, the state function F (u) = -cos u on [pi/2, 3 pi/2] and [pi/2, 5 pi/2] is discussed. For this, when it is necessary, the auxiliary problem which is equivalent to the main problem is introduced. The solution of the proposed problem permits constructing the weak solution of the main problem that conserves the entropy condition. In some cases, depending on the nature of the investigated problem a convex or a concave hull is constructed. Thus, the exact solutions are found by using these functions.
Açıklama
6th International Conference on Finite Difference Methods - Theory and Applications (FDM - T and A) -- JUN 18-23, 2014 -- Lozenetz, BULGARIA
Anahtar Kelimeler
First order nonlinear partial differential equations, Riemann problem, Characteristics, Weak solution, Shock wave, Convex and concave hull
Kaynak
Finite Difference Methods, Theory And Applications
WoS Q Değeri
N/A
Scopus Q Değeri
Q3
Cilt
9045
