On the Cauchy problem for effectively hyperbolic systems

On the Cauchy Problem for Nonlinear Hyperbolic Systems

This paper consider various examples of metrics which are contractive w.r.t. an evolution semigroup, and discusses the possibility of an abstract O.D.E. theory on metric spaces, with applications to hyperbolic systems. In particular, using a recently introduced deenition of Viscosity Solutions, it is shown how a strictly hyperbolic system of conservation laws can be reformulated as an abstract ...

the algorithm for solving the inverse numerical range problem

برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.

Precise Finite Speed and Uniqueness in the Cauchy Problem for Symmetrizable Hyperbolic Systems

Precise finite speed, in the sense of that the domain of influence is a subset of the union of influence curves through the support of the initial data is proved for hyperbolic systems symmetrized by pseudodifferential operators in the spatial variables. From this, uniqueness in the Cauchy problem at spacelike hypersurfaces is derived by a Hölmgren style duality argument. Sharp finite speed is ...

Stability of solutions to the Cauchy problem of symmetric hyperbolic systems

In this report we investigate the linear and nonlinear stability of stationary, constant solutions to the Cauchy problem of quasilinear, symmetric hyperbolic systems of equations. Writing the problem as u t = d X j=0 ? A 0j + "A 1j (x; t; u; ") with u(t = 0) = f(x); we say that the problem is non-linearly stable if, for " small enough, the solution u stays smooth for all t 0 and its maximum nor...

On the Riemann Problem for Non-conservative Hyperbolic Systems