A characteristic initial value problem for a strictly hyperbolic system
نویسندگان
چکیده
منابع مشابه
A characteristic initial value problem for a strictly hyperbolic system
Consider the system Autt +Cuxx = f(x,t), (x,t) ∈ T for u(x,t) in R2, where A and C are real constant 2× 2 matrices, and f is a continuous function in R2. We assume that detC ≠ 0 and that the system is strictly hyperbolic in the sense that there are four distinct characteristic curves Γi, i= 1, . . . ,4, in xt-plane whose gradients (ξ1i,ξ2i) satisfy det[Aξ2 1i+ Cξ2 2i]= 0. We allow the character...
متن کاملThe Initial Value Problem for Some Hyperbolic-dispersive System
We consider the initial value problem for some nonlinear hyperbolic and dispersive systems in one space dimension. Combining the classical energy method and the smoothing estimates for the Airy equation, we guarantee the time local well-posedness for this system. We also discuss the extension of our results to more general hyperbolic-dispersive system.
متن کاملInitial-Boundary Value Problem for Hyperbolic Equations
where Ji = 0 for x0 < 0. The problem is to find necessary and sufficient conditions on B(x, B) such that the initial-boundary value problem (1), (2), (3) is well-posed. Note that all theorems that a;re formulated below will also apply to the case when (1) is a general hyperbolic equation or a hyperbolic system of equations of arbitrary order provided that all components of the characteristic co...
متن کاملOn a characteristic initial value problem in plasma physics
The relativistic Vlasov-Maxwell system of plasma physics is considered with initial data on a past light cone. This characteristic initial value problem arises in a natural way as a mathematical framework to study the existence of solutions isolated from incoming radiation. Conservation laws and a priori estimates of smooth solutions are first derived in a formal way. In the spherically symmetr...
متن کاملPositive solutions for discrete fractional initial value problem
In this paper, the existence and uniqueness of positive solutions for a class of nonlinear initial value problem for a finite fractional difference equation obtained by constructing the upper and lower control functions of nonlinear term without any monotone requirement .The solutions of fractional difference equation are the size of tumor in model tumor growth described by the Gompertz f...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 2004
ISSN: 0161-1712,1687-0425
DOI: 10.1155/s0161171204308045