23,573 research outputs found
Infinite Horizon Noncooperative Differential Games with Non-Smooth Costs
In the present paper, we consider a class of two players infinite horizon
differential games, with piecewise smooth costs exponentially discounted in
time. Through the analysis of the value functions, we study in which cases it
is possible to establish the existence Nash equilibrium solutions in feedback
form. We also provide examples of piecewise linear costs whose corresponding
games have either infinitely many Nash equilibria or no solutions at all.Comment: 17 pages, 5 figure
Rigorous Numerical Verification of Uniqueness and Smoothness in a Surface Growth Model
Based on numerical data and a-posteriori analysis we verify rigorously the
uniqueness and smoothness of global solutions to a scalar surface growth model
with striking similarities to the 3D Navier--Stokes equations, for certain
initial data for which analytical approaches fail. The key point is the
derivation of a scalar ODE controlling the norm of the solution, whose
coefficients depend on the numerical data. Instead of solving this ODE
explicitly, we explore three different numerical methods that provide rigorous
upper bounds for its solutio
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