Strong instability of solitary waves for nonlinear Klein–Gordon equations and generalized Boussinesq equations
Sub-elliptic boundary value problems for quasilinear operators.
Sur le caractère bien posé des équations de Schrödinger non linéaires
Surface temperature determination from borehole measurements: Regularization and error estimates.
The Cauchy problem and Hadamard's example
The Cauchy problem for a system of Maxwell equations.
The Cauchy problem for operators with injective symbol in the Lebesgue space in a domain.
The Dirichlet boundary value problem for the system uxi-xj=0, j≠i.
The first boundary value problem for the vibrating string equation in domains with piecewise smooth boundary
The local ill-posedness of the modified KdV equation
The phase space of one generalized model by Oskolkov.
The well-posedness of the Dirichlet problem in the cylindric domain for the multidimensional wave equation.
The WKB method and geometric instability for nonlinear Schrödinger equations on surfaces
In this paper we are interested in constructing WKB approximations for the nonlinear cubic Schrödinger equation on a Riemannian surface which has a stable geodesic. These approximate solutions will lead to some instability properties of the equation.
Unique localization of unknown boundaries in a conducting medium from boundary measurements
We consider the problem of localizing an inaccessible piece of the boundary of a conducting medium , and a cavity contained in , from boundary measurements on the accessible part of . Assuming that is the given thermal flux for , and that the corresponding output datum is the temperature measured at a given time for , we prove that and are uniquely localized from knowledge of all possible pairs of input-output data . The same result holds when a mean value of the temperature...
Unique Localization of Unknown Boundaries in a Conducting Medium from Boundary Measurements
We consider the problem of localizing an inaccessible piece I of the boundary of a conducting medium Ω, and a cavity D contained in Ω, from boundary measurements on the accessible part A of ∂Ω. Assuming that g(t,σ) is the given thermal flux for (t,σ) ∈ (0,T) x A, and that the corresponding output datum is the temperature u(T0,σ) measured at a given time T0 for σ ∈ Aout ⊂ A, we prove that I and D are uniquely localized from knowledge of all possible pairs of input-output data . The same result...
Uniqueness and Free Interpolation for Logarithmic Potentials and the Cauchy Problem for the Laplace Equation in R2.
Задача Коши с видоизманенными начальными данными для обобщенного уравнения Эйлера-Пуассона-Дарбу
Задача с наклонной производной для волнового уравнения
Исследование условий корректности задачи Коши для одного уравнения
К теории многомерных эллиптических систем