Explicit definition of an exact measure for the semiflow of a first order partial differential equation. (English) Zbl 0624.35012

Brunovský, Pavol; Komorník, Jozef

Čas. Pěstování Mat. 111, 48-53 (1986).

From the authors’ summary: “The semiflow on C[0,1] generated by the initial problem \[ u_ t+c(x)u_ x=f(x,u),\quad x\in [0,1],\quad t\in [0,+\infty),\quad u(0,x)=v, \] is considered. A constructive definition of a scaling of the real line is given for proving exactness of the restrictions of the semiflow to subsets which are invariant with respect to the semiflow.”

Reviewer: Z.Kamont

MSC:

35F25	Initial value problems for nonlinear first-order PDEs
37-XX	Dynamical systems and ergodic theory

Keywords:

semiflow; initial problem; scaling; exactness of the restrictions; invariant