Constrained systems of conservation laws: a geometric theory

A Geometric Theory of Conservation Laws Which Change Type 1. Hyperbolic Conservation Laws in Modelling and Anal- Ysis

The study of systems of conservation laws has both geometric and analytic aspects. The structure of shocks and their relation to characteristics of the partial diierential equation are geometric in nature; these geometric pictures lead to admissibility criteria for shocks and the description of the propagation of a discontinuity as a Riemann solution. On the other hand, justiication of geometri...

Hyperbolic Systems of Conservation Laws

Its purpose is to provide an account of some recent advances in the mathematical theory of hyperbolic systems of conservation laws in one space dimension. After a brief review of basic concepts, we describe in detail the method of wave-front tracking approximation and present some of the latest results on uniqueness and stability of entropy weak solutions. 1-Review of basic theory. This chapter...

Hyperbolic Systems of Conservation Laws

Conservation laws are first order systems of quasilinear partial differential equations in divergence form; they express the balance laws of continuum physics for media with "elastic" response, in which internal dissipation is neglected. The absence of internal dissipation is manifested in the emergence of solutions with jump discontinuities across manifolds of codimension one, representing, in...

Error Estimate for Godunov Approximation of Locally Constrained Conservation Laws

Gate fidelity of self-adjoint gates constrained by conservation laws

Recent investigations show that conservation laws limit the accuracy of gate operations in quantum computing. The inevitable error under the angular momentum conservation law has been evaluated so far for the CNOT, Hadamard, and NOT gates for spin 1/2 qubits, while the SWAP gate has no constraint. Here, we consider arbitrary self-adjoint gates under arbitrary conservation laws from a geometrica...