On the nonconvergence of successive approximations in the theory of the equation
On the number of nodal solutions for a nonlinear elliptic problem on symmetric Riemannian manifolds.
On the operator related to Bessel heat equation.
On the Operator Solutions of Difference Equations
On the -growth of entire function solutions of Helmholtz equation.
On the periodic KdV equation in weighted Sobolev spaces
On the persistence of decorrelation in the theory of wave turbulence
We study the statistical properties of the solutions of the Kadomstev-Petviashvili equations (KP-I and KP-II) on the torus when the initial datum is a random variable. We give ourselves a random variable with values in the Sobolev space with big enough such that its Fourier coefficients are independent from each other. We assume that the laws of these Fourier coefficients are invariant under multiplication by for all . We investigate about the persistence of the decorrelation between the...
On the rectifiability of domains with finite perimeter
On the regularity for solutions of the micropolar fluid equations
On the relation between the Maslov-Whitham method and the weak asymptotics method
We explain the relation between the weak asymptotics method introduced by the author and V. M. Shelkovich and the classical Maslov-Whitham method for constructing approximate solutions describing the propagation of nonlinear solitary waves.
On the relative fundamental solutions for a second order differential operator on the Heisenberg group
Let Hₙ be the (2n+1)-dimensional Heisenberg group, let p,q ≥ 1 be integers satisfying p+q=n, and let , where X₁,Y₁,...,Xₙ,Yₙ,T denotes the standard basis of the Lie algebra of Hₙ. We compute explicitly a relative fundamental solution for L.
On the singular limit in a phase field model of phase transitions
On the singularities of 3-D Protter's problem for the wave equation.
On the singularities of solutions of partial differential equations with constant coefficients
On the S-matrix for Schrödinger operators with long-range potentials.
On the smoothness of the free boundary in a nonlocal one-dimensional parabolic free boundary value problem
We consider one-dimensional parabolic free boundary value problem with a nonlocal (integro-differential) condition on the free boundary. Results on Cm-smoothness of the free boundary are obtained. In particular, a necessary and sufficient condition for infinite differentiability of the free boundary is given.
On the solution of boundary value problems for sandwich plates
A mathematical model of the equilibrium problem of elastic sandwich plates is established. Using the theory of inequalities of Korn's type for a general class of elliptic systems the existence and uniqueness of a variational solution is proved.
On the solution of reaction-diffusion equations with double diffusivity.
On the solvability in Gevrey of a linear operator in two variables.
On the solvability of a variational inequality problem and application to a problem of two membranes.