ABSTRACT
Quasilinear partial differential equations such as symmetric hyperbolic systems of the first order, wave equations, the Korteweg–de Vries equation, Navier–Stokes and Euler equations, equations for compressible fluids, magnetohydrodynamic equations, coupled Maxwell and Dirac equations occur in mathematical physics. The issue of controllability of such quasilinear equations has been well established for deterministic equations. Kato presented a unified treatment of the Cauchy problem for various quasilinear equations that appear in mathematical physics, based on the theory of abstract evolution equations. An equivalent integral equation to the quasilinear system is obtained by showing the existence of random evolution system as in and applying Banach’s contraction principle to arrive at the controllability result.
