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- W2076412299 abstract "We investigate several 2D and 3D cases of the classical eigenvalue problem that arises in hydrodynamics and is referred to as the sloshing problem. In particular, for a domain W ⊂ R2 (canal's cross-section), where ∂W = F ∪ B and F (cross-section of the free surface of fluid) is an interval of the x-axis, whereas B (bottom's cross-section) is the graph of a negative function, the following result is proved. The fundamental eigenfunction u1 of the sloshing problem (the corresponding eigenvalue is simple) has monotonic traces on F and B; moreover, u1 attains its maximum and minimum values at the end-points of F. It is established that for the 2D (3D) ice-fishing problem with a single (circular) hole, the function u1 (both fundamental eigenfunctions) attains its maximum value at an inner point of F. A relationship between the high spots and hot spots theorems is considered." @default.
- W2076412299 created "2016-06-24" @default.
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- W2076412299 date "2009-03-19" @default.
- W2076412299 modified "2023-10-16" @default.
- W2076412299 title "‘High spots’ theorems for sloshing problems" @default.
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- W2076412299 doi "https://doi.org/10.1112/blms/bdp021" @default.
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