On the Influence of Lower Order Terms for Propagation of Analytic Singularities for Operators with Constant Coefficients.
On the inf-sup condition for higher order mixed FEM on meshes with hanging nodes
We consider higher order mixed finite element methods for the incompressible Stokes or Navier-Stokes equations with Qr-elements for the velocity and discontinuous -elements for the pressure where the order r can vary from element to element between 2 and a fixed bound . We prove the inf-sup condition uniformly with respect to the meshwidth h on general quadrilateral and hexahedral meshes with hanging nodes.
On the inhomogeneous nonlinear Schrödinger equation with harmonic potential and unbounded coefficient
By deriving a variant of interpolation inequality, we obtain a sharp criterion for global existence and blow-up of solutions to the inhomogeneous nonlinear Schrödinger equation with harmonic potential We also prove the existence of unstable standing-wave solutions via blow-up under certain conditions on the unbounded inhomogeneity and the power of nonlinearity, as well as the frequency of the wave.
On the initial value problem for a partial differential equation with operator coefficients.
On the initial-boundary value problems for a degenerate parabolic equation
For an equation of the type of porous media equation the Cauchy-Dirichlet and Cauchy-Neumann problems are considered. The existence and uniqueness results in the case of initial and boundary data are given.
On the instability of a class of periodic travelling wave solutions of the modified Boussinesq equation.
On the instability of ground states for a Davey-Stewartson system
On the instability of solitary-wave solutions for fifth-order water wave models.
On the instantaneous spreading for the Navier–Stokes system in the whole space
We consider the spatial behavior of the velocity field of a fluid filling the whole space () for arbitrarily small values of the time variable. We improve previous results on the spatial spreading by deducing the necessary conditions under more general assumptions on the localization of . We also give some new examples of solutions which have a stronger spatial localization than in the generic case.
On the Instantaneous Spreading for the Navier–Stokes System in the Whole Space
We consider the spatial behavior of the velocity field u(x, t) of a fluid filling the whole space () for arbitrarily small values of the time variable. We improve previous results on the spatial spreading by deducing the necessary conditions under more general assumptions on the localization of u. We also give some new examples of solutions which have a stronger spatial localization than in the generic case.
On the integral representation of superbiharmonic functions
We consider a nonnegative superbiharmonic function satisfying some growth condition near the boundary of the unit disk in the complex plane. We shall find an integral representation formula for in terms of the biharmonic Green function and a multiple of the Poisson kernel. This generalizes a Riesz-type formula already found by the author for superbihamonic functions satisfying the condition in the unit disk. As an application we shall see that the polynomials are dense in weighted Bergman...
On the integral representation of the solution to the Stokes system
On the interior boundary-value problem for the stationary Povzner equation with hard and soft interactions
The Povzner equation is a version of the nonlinear Boltzmann equation, in which the collision operator is mollified in the space variable. The existence of stationary solutions in is established for a class of stationary boundary-value problems in bounded domains with smooth boundaries, without convexity assumptions. The results are obtained for a general type of collision kernels with angular cutoff. Boundary conditions of the diffuse reflection type, as well as the given incoming profile, are...
On the interior differentiability of weak solutions of parabolic systems with quadratic growth nonlinearities
On the interior regularity of weak solutions of degenerate elliptic systems (the case < < )
On the interior regularity of weak solutions of non-stationary Navier-Stokes equations on a riemannian manifold
On the interior smoothness of solutions to second-order elliptic equations.
On the inverse problem of the Sturm-Liouville type for a linear elliptic partial differential equation with constant coefficients of the second order
On the inversion of pseudo-differential operators
On the iterated Green functions on a bounded domain and their related Kato class of potentials.