On the uniqueness of solutions in the class of increasing functions of a system describing the dynamics of a viscous weakly stratified fluid in three-dimensional space.
On the uniqueness of weak solutions for the 3D Navier-Stokes equations
On the variational inequality approach to compressible flows via hodograph method.
We study the flow of a compressible, stationary and irrotational fluid with wake, in a channel, around a convex symmetric profile, with assigned velocity q-infinity at infinity and q-s < q-infinity at the wake. In particular, we study the regularity of the free boundary (for a problem which has non-constant coefficients), in the hodograph plane.
On the Virasoro structure of symmetry algebras of nonlinear partial differential equations.
On the wave equations in the spacetime of a cosmic string
On the weak solutions of the forward problem in EEG.
On the Weak Solutions of the McKendrick Equation: Existence of Demography Cycles
We develop the qualitative theory of the solutions of the McKendrick partial differential equation of population dynamics. We calculate explicitly the weak solutions of the McKendrick equation and of the Lotka renewal integral equation with time and age dependent birth rate. Mortality modulus is considered age dependent. We show the existence of demography cycles. For a population with only one reproductive age class, independently of the stability of the weak solutions and after a transient time,...
On the asymptotic properties of solutions of the Navier-Stokes equations in the half-space.
On three-dimensional vortex patches
On Threshold Eigenvalues and Resonances for the Linearized NLS Equation
We prove the instability of threshold resonances and eigenvalues of the linearized NLS operator. We compute the asymptotic approximations of the eigenvalues appearing from the endpoint singularities in terms of the perturbations applied to the original NLS equation. Our method involves such techniques as the Birman-Schwinger principle and the Feshbach map.
On time-harmonic Maxwell equations with nonhomogeneous conductivities: Solvability and FE-approximation
The solvability of time-harmonic Maxwell equations in the 3D-case with nonhomogeneous conductivities is considered by adapting Sobolev space technique and variational formulation of the problem in question. Moreover, a finite element approximation is presented in the 3D-case together with an error estimate in the energy norm. Some remarks are given to the 2D-problem arising from geophysics.
On transformations of the Rabelo equations.
On two-dimensional finite-gap potential Schrödinger and Dirac operators with singular spectral curves.
On Uniqueness of Boundary Values of Solutions of a Problem Arising in Plasma Physics.
On variational approach to photometric stereo
On variational inequalities associated with the Navier-Stokes equation: Some bifurcation problems.
On various types of viscous two-fluid flows
Viscous two-fluid flows arise in different kinds of coating technologies. Frequently, the corresponding mathematical models represent two-dimensional free boundary value problems for the Navier-Stokes equations or their modifications. In this review article we present some results about nonisothermal stationary as well as about isothermal evolutionary viscous flow problems. The temperature-depending problems are characterized by coupled heat- and mass transfer and also by thermocapillary convection....
On wave functions in quantum mechanics
On wave functions in quantum mechanics. I
On wave functions in quantum mechanics. Part 3. A theory of quantum mechanics where wave functions are defined by means of surely fundamental observables