Boundary control of a symmetric hyperbolic system with nonlinear boundary conditions
Boundary control of the Maxwell dynamical system : lack of controllability by topological reasons
Boundary control of the Maxwell dynamical system: lack of controllability by topological reasons
The paper deals with a boundary control problem for the Maxwell dynamical system in a bounbed domain Ω ⊂ R3. Let ΩT ⊂ Ω be the subdomain filled by waves at the moment T, T* the moment at which the waves fill the whole of Ω. The following effect occurs: for small enough T the system is approximately controllable in ΩT whereas for larger T < T* a lack of controllability is possible. The subspace of unreachable states is of finite dimension determined by topological characteristics of ΩT.
Boundary control theory for hyperbolic and parabolic partial differential equations with constant coefficients
Boundary controllability for the nonlinear Korteweg-de Vries equation on any critical domain
Boundary controllability of a chain of serially connected Euler-Bernoulli beams with interior masses.
Boundary controllability of hyperbolic equations.
Boundary eigencurve problems involving the biharmonic operator
The aim of this paper is to study the spectrum of the fourth order eigenvalue boundary value problem ⎧Δ²u = αu + βΔu in Ω, ⎨ ⎩u = Δu = 0 on ∂Ω. where (α,β) ∈ ℝ². We prove the existence of a first nontrivial curve of this spectrum and we give its variational characterization. Moreover we prove some properties of this curve, e.g., continuity, convexity, and asymptotic behavior. As an application, we study the non-resonance of solutions below...
Boundary eigencurve problems involving the -Laplacian operator.
Boundary estimates for certain degenerate and singular parabolic equations
We study the boundary behavior of non-negative solutions to a class of degenerate/singular parabolic equations, whose prototype is the parabolic -Laplacian equation. Assuming that such solutions continuously vanish on some distinguished part of the lateral part of a Lipschitz cylinder, we prove Carleson-type estimates, and deduce some consequences under additional assumptions on the equation or the domain. We then prove analogous estimates for non-negative solutions to a class of degenerate/singular...
Boundary estimates for solutions of Monge-Ampère equations in the plane
Boundary estimates for solutions of nonlinear degenerate parabolic systems.
Boundary feedback stabilization of a hybrid PDE-ODE system.
Boundary higher integrability for the gradient of distributional solutions of nonlinear systems
Boundary homogenization for a quasi-linear elliptic problem with Dirichlet boundary conditions posed on small inclusions distributed on the boundary.
Boundary integral equations and modified Green's functions
Boundary integral equations for mixed boundary value problems in polygonal domains and Galerkin approximation
Boundary integral equations of the logarithmic potential theory for domains with peaks
Integral equations of boundary value problems of the logarithmic potential theory for a plane domain with several peaks at the boundary are studied. We present theorems on the unique solvability and asymptotic representations for solutions near peaks. We also find kernels of the integral operators in a class of functions with a weak power singularity and describe classes of uniqueness.
Boundary integral formulae for the reconstruction of electric and electromagnetic inhomogeneities of small volume
In this paper we discuss the approximate reconstruction of inhomogeneities of small volume. The data used for the reconstruction consist of boundary integrals of the (observed) electromagnetic fields. The numerical algorithms discussed are based on highly accurate asymptotic formulae for the electromagnetic fields in the presence of small volume inhomogeneities.
Boundary integral formulae for the reconstruction of electric and electromagnetic inhomogeneities of small volume
In this paper we discuss the approximate reconstruction of inhomogeneities of small volume. The data used for the reconstruction consist of boundary integrals of the (observed) electromagnetic fields. The numerical algorithms discussed are based on highly accurate asymptotic formulae for the electromagnetic fields in the presence of small volume inhomogeneities.