Asymptotic stability in L¹ of a transport equation
We study the asymptotic behaviour of solutions of a transport equation. We give some sufficient conditions for the complete mixing property of the Markov semigroup generated by this equation.
Asymptotic stability of a linear Boltzmann-type equation
We present a new necessary and sufficient condition for the asymptotic stability of Markov operators acting on the space of signed measures. The proof is based on some special properties of the total variation norm. Our method allows us to consider the Tjon-Wu equation in a linear form. More precisely a new proof of the asymptotic stability of a stationary solution of the Tjon-Wu equation is given.
Asymptotic stability of a partial differential equation with an integral perturbation
We study the asymptotic behaviour of the Markov semigroup generated by an integro-partial differential equation. We give new sufficient conditions for asymptotic stability of this semigroup.
Asymptotic stability of an integro-differential equation of parabolic type
Asymptotic stability of the extended Tjon-Wu model.
Asymptotic stability of wave equations with memory and frictional boundary dampings
This work is concerned with stabilization of a wave equation by a linear boundary term combining frictional and memory damping on part of the boundary. We prove that the energy decays to zero exponentially if the kernel decays exponentially at infinity. We consider a slightly different boundary condition than the one used by M. Aassila et al. [Calc. Var. 15, 2002]. This allows us to avoid the assumption that the part of the boundary where the feedback is active is strictly star-shaped. The result...
Asymptotic stability results for certain integral equations.
Asymptotically almost periodic and almost periodic solutions for a class of partial integro-differential equations.
Asymptotically almost periodic solutions for abstract partial neutral integro-differential equation.
Asymptotics for large time of solutions to nonlinear system associated with the penetration of a magnetic field into a substance
The nonlinear integro-differential system associated with the penetration of a magnetic field into a substance is considered. The asymptotic behavior as of solutions for two initial-boundary value problems are studied. The problem with non-zero conditions on one side of the lateral boundary is discussed. The problem with homogeneous boundary conditions is studied too. The rates of convergence are given. Results presented show the difference between stabilization characters of solutions of these...
Asymptotics of a solution of a nonlinear system of diffusion of a magnetic field into a substance.
Asymptotics of integrodifferential models with integrable kernels II.
Asymptotics of integrodifferential models with integrable kernels.
Asymptotics of permutations with nearly periodic patterns of rises and falls.
Automorphisms of C commuting with partial integration operators in a rectangle
Convolutional representations of the commutant of the partial integration operators in the space of continuous functions in a rectangle are found. Necessary and sufficient conditions are obtained for two types of representing functions, to be the operators in the commutant continuous automorphisms. It is shown that these conditions are equivalent to the requirement that the considered representing functions be joint cyclic elements of the partial integration operators.
Backward Differentiation Type Formulas for Volterra Integral Equations of the Second Kind.
Backward Euler type methods for parabolic integro-differential equations in Banach space
Backward solutions to nonlinear integro-differential systems
In this paper, we show the backward uniqueness in time of solutions to nonlinear integro-differential systems with Neumann or Dirichlet boundary conditions. We also discuss reasonable physical interpretations for our conclusions.
Behaviour of solutions of an integral equation
Berechnung der ebenen Potentialströmung von rotierenden radialen Profilgittern