Initial Boundary Value Problems for Hyperbolic Partial Differential Equations
نویسنده
چکیده
1, Differential equations in one space dimension. The simplest hyperbolic differential equation is given by (1.1) du/dt = cdu/dx, where c is a constant, Its general solution is u(x, t) — F(x + ci), i.e., it is constant along the "characteristic lines" x + ct = const (see Figure 1). Therefore, if we u(l,t) = g(t) u(0,t)*g(t want to determine the solution of (1.1) in the region 0 ^ x ^ 1, t ja 0, we have to describe initial conditions (1.2) u(x,0)=f(x), for t = 0 and boundary conditions u(l,t) = g(t) ifc>0, (1.3) <0,t) = g(t) ifc<0,
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