Weak Solutions for a Simple Hyperbolic System
Copyright policy )Weak Solutions for a Simple Hyperbolic System
The authors study the Cauchy problem for a semilinear hyperbolic system with the quadratic nonlinear term of special kind. They demonstrate existence and uniqueness of weak solutions. The direct method used is guided by the theory of measure-valued diffusions. This method seems to be more effective than the method of characteristics, and has the advantage that it leads immediately to the McKean representation without recourse to Itô's formula. The authors also conduct numerical analysis using both probabilistic simulation of the branching process and finite difference methods.
- University of Nottingham United Kingdom
branching processes, Martingales with continuous parameter, finite differnce methods, Martingales, First-order nonlinear hyperbolic equations, Weak solutions, probabilistic simulation, 60J27, QA273, martingales, 35L35, Branching processses, travelling waves, 60G44, Initial value problems for first-order hyperbolic systems, quadratic nonlinear term, Travelling waves, Continuous-time Markov processes on discrete state spaces, semilinear hyperbolic system
branching processes, Martingales with continuous parameter, finite differnce methods, Martingales, First-order nonlinear hyperbolic equations, Weak solutions, probabilistic simulation, 60J27, QA273, martingales, 35L35, Branching processses, travelling waves, 60G44, Initial value problems for first-order hyperbolic systems, quadratic nonlinear term, Travelling waves, Continuous-time Markov processes on discrete state spaces, semilinear hyperbolic system
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