On self-similarity and stationary problem for fragmentation and coagulation models
On some differential inequalities and the uniqueness of global semiclassical solutions to the Cauchy problem for weakly-coupled systems.
On the absence of Poincaré lemma in tangential Cauchy-Riemann complexes
On the age-dependent predator-prey model
The paper deals with the description of a model which is the synthesis of two classical models, the Lotka-Volterra and McKendrick-von Foerster models. The existence and uniqueness of the solution for the new population problem are proved, as well the asymptotic periodicity but under some simplifying assumptions.
On the Cauchy problem for linear partial differential-functional equations of first order
On the Chaplighin method for partial differential equations of the first order
On the Chaplygin method for partial differential-functional equations of the first order
On the characteristics for a system of partial differential equations of the first order in a special case
On the dense trajectory of Lasota equation.
On the distribution of free path lengths for the periodic Lorentz gas II
On the distribution of free path lengths for the periodic Lorentz gas II
Consider the domain and let the free path length be defined as In the Boltzmann-Grad scaling corresponding to , it is shown that the limiting distribution of is bounded from below by an expression of the form C/t, for some C> 0. A numerical study seems to indicate that asymptotically for large t, . This is an extension of a previous work [J. Bourgain et al., Comm. Math. Phys.190 (1998) 491-508]. As a consequence, it is proved that the linear Boltzmann type transport equation is inappropriate...
On the existence and the regularity of an initial boundary problem of vorticity equation
On the existence of an invariant measure for the dynamical system generated by partial differential equation
On the existence of generalized solutions of nonlinear first order partial differential-functional equations in two independent variables
On the existence of global holomorphic solutions of differential equations with complex parameters
On the existence of variations, possibly with pointwise gradient constraints
We propose a necessary and sufficient condition about the existence of variations, i.e., of non trivial solutions to the differential inclusion .
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 Landau approximation in plasma physics
On the left linear Riemann problem in Clifford analysis.
On the linear force-free fields in bounded and unbounded three-dimensional domains