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In this paper we consider a class of distributed parameter systems (partial differential equations) determined by strongly nonlinear operator valued measures in the setting of the Gelfand triple V ↪ H ↪ V* with continuous and dense embeddings where H is a separable Hilbert space and V is a reflexive Banach space with dual V*. The system is given by dx + A(dt,x) = f(t,x)γ(dt) + B(t)u(dt), x(0) = ξ, t ∈ I ≡ [0,T] where A is a strongly nonlinear operator valued measure...

Partial differential equations with piecewise constant delay.

Wiener, Joseph, Debnath, Lokenath (1991)

International Journal of Mathematics and Mathematical Sciences

Periodic solutions of abstract differential equations: the Fourier method

Leopold Herrmann (1980)

Czechoslovak Mathematical Journal

Perron-Frobenius operators and the Klein-Gordon equation

Francisco Canto-Martín, Håkan Hedenmalm, Alfonso Montes-Rodríguez (2014)

Journal of the European Mathematical Society

For a smooth curve $Γ$ and a set $Λ$ in the plane $ℝ^{2}$ , let $A C (Γ; Λ)$ be the space of finite Borel measures in the plane supported on $Γ$ , absolutely continuous with respect to the arc length and whose Fourier transform vanishes on $Λ$ . Following [12], we say that $(Γ, Λ)$ is a Heisenberg uniqueness pair if $A C (Γ; Λ) = {0}$ . In the context of a hyperbola $Γ$ , the study of Heisenberg uniqueness pairs is the same as looking for uniqueness sets $Λ$ of a collection of solutions to the Klein-Gordon equation. In this work, we mainly address the...

Propagation de singularités pour des problèmes aux limites d'ordre 2

R. B. Melrose, J. Sjöstrand (1977/1978)

Séminaire Équations aux dérivées partielles (Polytechnique)

Propagation of waves in a randomly stratified medium: an inverse problem.

Blagoveshchenskij, A.S. (2009)

Sibirskij Matematicheskij Zhurnal

Quelques résultats de non résolubilité locale pour des équations hyperboliques

Ferruccio Colombini (1987)

Journées équations aux dérivées partielles

Remarques sur la caractérisation des problèmes mixtes bien posés pour un opérateur hyperbolique

Jacques Chazarain, Alain Piriou (1972)

Séminaire Jean Leray

Schwinger-Fronsdal theory of abelian tensor gauge fields.

Guttenberg, Sebastian, Savvidy, George (2008)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Sets of removable singularities of an equation

Miroslav Dont (1973)

Acta Universitatis Carolinae. Mathematica et Physica

Sharp regularity theory for second order hyperbolic equations of Neumann type

Irena Lasiecka, Roberto Triggiani (1989)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

This note provides sharp regularity results for general, time-independent, second order, hyperbolic equations with non-homogeneous data of Neumann type.

Single input controllability of a simplified fluid-structure interaction model

Yuning Liu, Takéo Takahashi, Marius Tucsnak (2013)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we study a controllability problem for a simplified one dimensional model for the motion of a rigid body in a viscous fluid. The control variable is the velocity of the fluid at one end. One of the novelties brought in with respect to the existing literature consists in the fact that we use a single scalar control. Moreover, we introduce a new methodology, which can be used for other nonlinear parabolic systems, independently of the techniques previously used for the linearized problem....

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On the hyperbolic linear functional equations.

On the stabilization of wave-advection coupling. (Sur la stabilisation d'un couplage ondes-advection.)

On the validity of Huygens' principle for second order partial differential equations with four independent variables. II. A sixth necessary condition

On the validity of Huygens' principle for second order partial differential equations with four independent variables. Part I : derivation of necessary conditions

On unique solvability of the periodic problem in the plane for linear hyperbolic equations.

Optimal control of systems determined by strongly nonlinear operator valued measures