Variational data assimilation for discrete Burgers equation.
Analysis of the self-similar solutions of a generalized Burgers equation with nonlinear damping.
Positive solutions for elliptic problems with critical indefinite nonlinearity in bounded domains.
Optimal control of linearized compressible Navier–Stokes equations
We study an optimal boundary control problem for the two dimensional unsteady linearized compressible Navier–Stokes equations in a rectangle. The control acts through the Dirichlet boundary condition. We first establish the existence and uniqueness of the solution for the two-dimensional unsteady linearized compressible Navier–Stokes equations in a rectangle with inhomogeneous Dirichlet boundary data, not necessarily smooth. Then, we prove the existence and uniqueness of the optimal solution over...
Unbounded viscosity solutions of hybrid control systems
We study a hybrid control system in which both discrete and continuous controls are involved. The discrete controls act on the system at a given set interface. The state of the system is changed discontinuously when the trajectory hits predefined sets, namely, an autonomous jump set or a controlled jump set where controller can choose to jump or not. At each jump, trajectory can move to a different Euclidean space. We allow the cost functionals to be unbounded with certain growth and hence the...
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