Displaying similar documents to “Some qualitative problems in the theory of second order partial differential equations”

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.

Stability analysis for acoustic waveguides. Part 3: impedance boundary conditions

Leszek Demkowicz, Jay Gopalakrishnan, Norbert Heuer (2024)

Applications of Mathematics

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A model two-dimensional acoustic waveguide with lateral impedance boundary conditions (and outgoing boundary conditions at the waveguide outlet) is considered. The governing operator is proved to be bounded below with a stability constant inversely proportional to the length of the waveguide. The presence of impedance boundary conditions leads to a non self-adjoint operator which considerably complicates the analysis. The goal of this paper is to elucidate these complications and tools...