The Cauchy problem and Hadamard's example
The Cauchy problem for a system of Maxwell equations.
The Cauchy problem for operators with injective symbol in the Lebesgue space in a domain.
The Dirichlet boundary value problem for the system uxi-xj=0, j≠i.
The first boundary value problem for the vibrating string equation in domains with piecewise smooth boundary
The local ill-posedness of the modified KdV equation
The phase space of one generalized model by Oskolkov.
The well-posedness of the Dirichlet problem in the cylindric domain for the multidimensional wave equation.
The WKB method and geometric instability for nonlinear Schrödinger equations on surfaces
In this paper we are interested in constructing WKB approximations for the nonlinear cubic Schrödinger equation on a Riemannian surface which has a stable geodesic. These approximate solutions will lead to some instability properties of the equation.