| 000 | 03210nam a22005175i 4500 | ||
|---|---|---|---|
| 001 | 978-3-031-02415-3 | ||
| 003 | DE-He213 | ||
| 005 | 20240730163457.0 | ||
| 007 | cr nn 008mamaa | ||
| 008 | 220601s2019 sz | s |||| 0|eng d | ||
| 020 |
_a9783031024153 _9978-3-031-02415-3 |
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| 024 | 7 |
_a10.1007/978-3-031-02415-3 _2doi |
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| 072 | 7 |
_aPB _2bicssc |
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_aPB _2thema |
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_a510 _223 |
| 100 | 1 |
_aRamm, Alexander G. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut _978779 |
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| 245 | 1 | 0 |
_aSymmetry Problems _h[electronic resource] : _bThe Navier-Stokes Problem / _cby Alexander G. Ramm. |
| 250 | _a1st ed. 2019. | ||
| 264 | 1 |
_aCham : _bSpringer International Publishing : _bImprint: Springer, _c2019. |
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| 300 |
_aXIV, 71 p. _bonline resource. |
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| 336 |
_atext _btxt _2rdacontent |
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| 337 |
_acomputer _bc _2rdamedia |
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| 338 |
_aonline resource _bcr _2rdacarrier |
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| 347 |
_atext file _bPDF _2rda |
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| 490 | 1 |
_aSynthesis Lectures on Mathematics & Statistics, _x1938-1751 |
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| 505 | 0 | _aPreface -- Introduction -- Necessary and Sufficient Conditions for a Scatterer to be Spherically Symmetric -- Symmetry Problems for the Helmholtz Equation -- Other Symmetry Problems -- Solution to the Navier--Stokes Problem -- Inverse Problem of Potential Theory -- Bibliography -- Author's Biography . | |
| 520 | _aThis book gives a necessary and sufficient condition in terms of the scattering amplitude for a scatterer to be spherically symmetric. By a scatterer we mean a potential or an obstacle. It also gives necessary and sufficient conditions for a domain to be a ball if an overdetermined boundary problem for the Helmholtz equation in this domain is solvable. This includes a proof of Schiffer's conjecture, the solution to the Pompeiu problem, and other symmetry problems for partial differential equations. It goes on to study some other symmetry problems related to the potential theory. Among these is the problem of "invisible obstacles." In Chapter 5, it provides a solution to the Navier‒Stokes problem in ℝ³. The author proves that this problem has a unique global solution if the data are smooth and decaying sufficiently fast. A new a priori estimate of the solution to the Navier‒Stokes problem is also included. Finally, it delivers a solution to inverse problem of the potential theory without the standard assumptions about star-shapeness of the homogeneous bodies. | ||
| 650 | 0 |
_aMathematics. _911584 |
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| 650 | 0 |
_aStatistics . _931616 |
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| 650 | 0 |
_aEngineering mathematics. _93254 |
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| 650 | 1 | 4 |
_aMathematics. _911584 |
| 650 | 2 | 4 |
_aStatistics. _914134 |
| 650 | 2 | 4 |
_aEngineering Mathematics. _93254 |
| 710 | 2 |
_aSpringerLink (Online service) _978780 |
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| 773 | 0 | _tSpringer Nature eBook | |
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_iPrinted edition: _z9783031002618 |
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_iPrinted edition: _z9783031012877 |
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_iPrinted edition: _z9783031035432 |
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_aSynthesis Lectures on Mathematics & Statistics, _x1938-1751 _978781 |
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| 856 | 4 | 0 | _uhttps://doi.org/10.1007/978-3-031-02415-3 |
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| 942 | _cEBK | ||
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