On the relation between the Borel sum and the classical solution of the Cauchy problem for certain partial differential 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 Relation between the S-matrix and the Spectrum of the Interior Laplacian
The main results of this paper are: 1) a proof that a necessary condition for 1 to be an eigenvalue of the S-matrix is real analyticity of the boundary of the obstacle, 2) a short proof that if 1 is an eigenvalue of the S-matrix, then k² is an eigenvalue of the Laplacian of the interior problem, and that in this case there exists a solution to the interior Dirichlet problem for the Laplacian, which admits an analytic continuation to the whole space ℝ³ as an entire function.
On the relation of delay equations to first-order hyperbolic partial differential equations
This paper establishes the equivalence between systems described by a single first-order hyperbolic partial differential equation and systems described by integral delay equations. System-theoretic results are provided for both classes of systems (among them converse Lyapunov results). The proposed framework can allow the study of discontinuous solutions for nonlinear systems described by a single first-order hyperbolic partial differential equation under the effect of measurable inputs acting on...
On the relationship between difference and projection-difference methods
On the Relative Completeness of the Generalized Eigenvectors of Elliptic Eigenvalue Problems with Indefinite Weight Functions.
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 relativistic calculation of the Lamb shift
A relativistic calculation of the Lamb shift, using the classical field created by the Dirac transition currents, is proposed.
On the remainder in the Weyl formula for the Euclidean disk
We prove a 2-terms Weyl formula for the counting function of the spectrum of the Laplace operator in the Euclidean disk with a sharp remainder estimate .
On the representation of non-negative solutions of linear parabolic systems of partial differential equations
On the result of He concerning the smoothness of solutions to the Navier-Stokes equations.
On the Riemann-Hilbert problem in the domain with a nonsmooth boundary.
On the rigidity of minimal mass solutions to the focusing mass-critical NLS for rough initial data.
On the role of boundary conditions for CIP stabilization of higher order finite elements.
On the role of the equal-area condition in internal layer stationary solutions to a class of reaction-diffusion systems.
On the scattering in Gevrey classes for the subcritical Hartree and Schrödinger equations
On the Scattering Matrix for N-Particle Hamiltonians
On the scattering theory of the Laplacian with a periodic boundary condition. II. Additional channels of scattering.
On the scattering theory of the Laplacian with a periodic boundary condition. I. Existence of wave operators.
On the Schauder estimates of solutions to parabolic equations