Displaying similar documents to “Stability analysis for acoustic waveguides. Part 3: impedance boundary conditions”

The BV solution of the parabolic equation with degeneracy on the boundary

Huashui Zhan, Shuping Chen (2016)

Open Mathematics

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Consider a parabolic equation which is degenerate on the boundary. By the degeneracy, to assure the well-posedness of the solutions, only a partial boundary condition is generally necessary. When 1 ≤ α < p – 1, the existence of the local BV solution is proved. By choosing some kinds of test functions, the stability of the solutions based on a partial boundary condition is established.

On the solvability of the Lyapunov equation for nonselfadjoint differential operators of order 2m with nonlocal boundary conditions

Aris Tersenov (2001)

Annales Polonici Mathematici

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This paper is devoted to the solvability of the Lyapunov equation A*U + UA = I, where A is a given nonselfadjoint differential operator of order 2m with nonlocal boundary conditions, A* is its adjoint, I is the identity operator and U is the selfadjoint operator to be found. We assume that the spectra of A* and -A are disjoint. Under this restriction we prove the existence and uniqueness of the solution of the Lyapunov equation in the class of bounded operators.