We consider Hamilton--Jacobi equations, where the Hamiltonian depends discontinuously on both the spatial and temporal location. Our main results is the existence of viscosity solution to the Cauchy problem, and that the ...

We consider doubly nonlinear anisotropic degenerate parabolic equations, supplemented with an initial condition and a homogeneous Dirichlet boundary condition. We introduce a notion of entropy solution and prove that the ...

The stochastic integral representation for an arbitrary random variable in a standard $L_2$-space is considered in a case of a general $L_2$-continuous martingale as integrator. In relation to this, a certain stochastic ...

We give a short introduction to some of the theory and methods involved in stochastic control with partial observation. As an illustration we use the stochastic maximum principle and the Kalman-Bucy filter to solve explicitly ...

We consider a generalized hyperelastic-rod wave equation (or generalized Camassa--Holm equation) describing nonlinear dispersive waves in compressible hyperelastic rods. We establish existence of a strongly continuous ...

We investigate a class of optimal consumption problems where the wealth X(t) at time t is given by a stochastic differential delay equation with a parameter. Not only the present value X(t), but also X(t-\delta) and some ...

While it is common knowledge that portfolio separation in a continuous-time lognormal market is due to the basic properties of the normal distribution, the usual exposition found in text books relies on dynamic programming ...

The present work is a numerical investigation on waves generated by a pressure disturbance moving at constant speed in a channel with a variable cross-channel depth profile. The channel profile, which is uniform in the ...