scholarly journals Local Exponential $H^2$ Stabilization of a $2\times2$ Quasilinear Hyperbolic System Using Backstepping

2013 ◽  
Vol 51 (3) ◽  
pp. 2005-2035 ◽  
Author(s):  
Jean-Michel Coron ◽  
Rafael Vazquez ◽  
Miroslav Krstic ◽  
Georges Bastin
Keyword(s):  
Hyperbolic System ◽  
Quasilinear Hyperbolic System

scholarly journals Life-Span of Classical Solutions to Hyperbolic Inverse Mean Curvature Flow

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Zenggui Wang
Keyword(s):  
Cauchy Problem ◽  
Life Span ◽  
Hyperbolic System ◽  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Classical Solutions ◽  
Quasilinear Hyperbolic System ◽  
Inverse Mean Curvature Flow ◽  
The Cauchy Problem

In this paper, we investigate the life-span of classical solutions to hyperbolic inverse mean curvature flow. Under the condition that the curve can be expressed in the form of a graph, we derive a hyperbolic Monge–Ampère equation which can be reduced to a quasilinear hyperbolic system in terms of Riemann invariants. By the theory on the local solution for the Cauchy problem of the quasilinear hyperbolic system, we discuss life-span of classical solutions to the Cauchy problem of hyperbolic inverse mean curvature.

scholarly journals Mixed problem for quasilinear hyperbolic system with coefficients functionally dependent on solution

2017 ◽  
Vol 25 (3) ◽  
pp. 215
Author(s):  
Małgorzata Zdanowicz ◽  
Zbigniew Peradzyński
Keyword(s):  
Banach Space ◽  
Initial Data ◽  
Mixed Problem ◽  
Hyperbolic System ◽  
Quasilinear Hyperbolic System ◽  
Nonlinear Operators ◽  
Uniqueness And Existence ◽  
Class C ◽  
Additional Assumptions

Abstract The mixed problem for quasilinear hyperbolic system with coefficients functionally dependent on the solution is studied. We assume that the coefficients are continuous nonlinear operators in the Banach space C1(ℝ) satisfying some additional assumptions. Under these assumptions we prove the uniqueness and existence of local in time C1 solution, provided that the initial data are also of class C1.

Sign in / Sign up

Export Citation Format

Share Document