Stability of ultraproducts of linear topological spaces
Z. Kadelburg, S. Radenović (1988)
Matematički Vesnik
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Displaying similar documents to “Some qualitative problems in the theory of second order partial differential equations”
Stability of ultraproducts of linear topological spaces
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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.
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Stability analysis for acoustic waveguides. Part 3: impedance boundary conditions
Leszek Demkowicz, Jay Gopalakrishnan, Norbert Heuer (2024)
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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...