Special Session 4: Nonlinear PDEs and Control Theory with Applications

In the large context of nonlinear evolution equations we will focus on systems of PDEs which exhibit a hyperbolic or parabolic-hyperbolic structure. The topics of this special session will revolve around qualitative and quantitative properties of solutions to these equations, such as existence and uniqueness, regularity of solutions, and long time asymptotic behavior. Associated control theoretic questions such as stabilization, controllability and optimal control will be addressed as well. Both bounded and unbounded domain problems will be under considerations. Of special interest in our discussions are interactions involving nonlinearity and geometry . Several methods available for investigation of such problems will be presented. We anticipate also to discuss specific problems that arise in applications such as nonlinear acoustics, traveling waves in elasticity and viscoelasticity, plasma dynamics, and semiconductors.