We consider the Dirac equation, written in polar formalism, presence of general Coulomb-like potentials, that is, potentials arising from time component vector potential and depending only on radial coordinate, order to study conditions integrability, given as some specific form for solution: we find angular dependence can always be integrated, while is reduced finding solution a Riccati equati...

We study here the Zakharov-Kuznetsov equation in dimension 2 2 , alttext="3"> 3 encoding="application/x-tex">3</mml:annotatio...

In this paper we establish the space-like strong unique continuation for nonlocal equations of type (∂t−Δ)su=Vu, 0<s<1. The proof our main result, Theorem 1.1, is achieved via a conditional elliptic doubling property solutions to appropriate extension problem, followed by blowup analysis.

The current study investigates the solvability conditions and general solution of three symmetrical systems coupled Sylvester-like quaternion matrix equations. Accordingly, necessary sufficient for consistency these are determined, solutions thereby deduced. An algorithm a numerical example constructed over quaternions to validate results this paper.

In this paper we present a Krylov acceleration technique for nonlinear PDEs. As a `precon-ditioner' we use nonlinear multigrid schemes, like FAS 1]. The beneets of the combination of nonlinear multigrid and the new proposed accelerator is shown for diicult nonlinear ellip-tic scalar problems, like the Bratu problem and for systems of nonlinear equations, like the Navier-Stokes equations.

Unbounded stochastic control problems may lead to Hamilton-Jacobi-Bellman equations whose Hamiltonians are not always defined, especially when the diffusion term is unbounded with respect to the control. We obtain existence and uniqueness of viscosity solutions growing at most like o(1+ |x|p) at infinity for such HJB equations and more generally for degenerate parabolic equations with a superli...