| 000 | 04606nam a22006731i 4500 | ||
|---|---|---|---|
| 001 | 8661826 | ||
| 003 | IEEE | ||
| 005 | 20200413152931.0 | ||
| 006 | m eo d | ||
| 007 | cr bn |||m|||a | ||
| 008 | 190402s2019 cau foab 000 0 eng d | ||
| 020 |
_a9781681735061 _qelectronic |
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| 020 |
_z9781681735078 _qhardcover |
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| 020 |
_z9781681735054 _qpaperback |
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| 024 | 7 |
_a10.2200/S00898ED1V01Y201902MAS023 _2doi |
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| 035 | _a(CaBNVSL)thg00978683 | ||
| 035 | _a(OCoLC)1091193877 | ||
| 040 |
_aCaBNVSL _beng _erda _cCaBNVSL _dCaBNVSL |
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| 050 | 4 |
_aQA374 _b.R367 2019eb |
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| 082 | 0 | 4 |
_a518/.64 _223 |
| 100 | 1 |
_aRamm, A. G. _q(Alexander G.), _eauthor. |
|
| 245 | 1 | 0 |
_aSymmetry problems : _bthe Navier-Stokes problem / _cAlexander G. Ramm. |
| 246 | 3 | 0 | _aNavier-Stokes problem. |
| 264 | 1 |
_a[San Rafael, California] : _bMorgan & Claypool, _c[2019] |
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| 300 | _a1 PDF (xiv, 71 pages). | ||
| 336 |
_atext _2rdacontent |
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| 337 |
_aelectronic _2isbdmedia |
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| 338 |
_aonline resource _2rdacarrier |
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| 490 | 1 |
_aSynthesis lectures on mathemathics and statistics, _x1938-1743 ; _v#23 |
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| 538 | _aMode of access: World Wide Web. | ||
| 538 | _aSystem requirements: Adobe Acrobat Reader. | ||
| 500 | _aPart of: Synthesis digital library of engineering and computer science. | ||
| 504 | _aIncludes bibliographical references (pages 65-69). | ||
| 505 | 0 | _a1. Introduction -- 2. Necessary and sufficient conditions for a scatterer to be spherically symmetric -- 2.1. Scattering by potentials -- 2.2. Scattering by obstacles | |
| 505 | 8 | _a3. Symmetry problems for the Helmholtz equation -- 3.1. A general symmetry problem -- 3.2. Old symmetry problem -- 3.3. Necessary and sufficient conditions for S to be a sphere -- 3.4. The Pompeiu problem | |
| 505 | 8 | _a4. Other symmetry problems -- 4.1. Volume potential -- 4.2. Surface potential -- 4.3. Invisible obstacles | |
| 505 | 8 | _a5. Solution to the Navier-Stokes problem -- 5.1. A new approach -- 5.2. Construction of G -- 5.3. Solution to integral equation for v satisfies NS equations -- 5.4. Uniqueness of the solution to the integral equation -- 5.5. Existence of the solution to integral equation -- 5.6. Energy of the solution -- 5.7. Auxiliary estimates -- 5.8. Proof of the uniqueness of the solution -- 5.9. Proof of the existence of the solution -- 5.10. Convolution and positiveness of distributions | |
| 505 | 8 | _a6. Inverse problem of potential theory -- 6.1. Statement of the problem -- 6.2. Proofs. | |
| 506 | _aAbstract freely available; full-text restricted to subscribers or individual document purchasers. | ||
| 510 | 0 | _aCompendex | |
| 510 | 0 | _aINSPEC | |
| 510 | 0 | _aGoogle scholar | |
| 510 | 0 | _aGoogle book search | |
| 520 | 3 | _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. | |
| 530 | _aAlso available in print. | ||
| 588 | _aTitle from PDF title page (viewed on April 2, 2019). | ||
| 650 | 0 | _aHelmholtz equation. | |
| 650 | 0 | _aNavier-Stokes equations. | |
| 650 | 0 | _aScattering (Mathematics) | |
| 653 | _aHelmholtz equation | ||
| 653 | _asymmetry problems | ||
| 653 | _aNavier--Stokes problem | ||
| 653 | _aInverse problem of potential theory | ||
| 776 | 0 | 8 |
_iPrint version: _z9781681735078 _z9781681735054 |
| 830 | 0 | _aSynthesis digital library of engineering and computer science. | |
| 830 | 0 |
_aSynthesis lectures on mathemathics and statistics ; _v#23. |
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| 856 | 4 | 2 |
_3Abstract with links to resource _uhttps://ieeexplore.ieee.org/servlet/opac?bknumber=8661826 |
| 856 | 4 | 0 |
_3Abstract with links to full text _uhttps://doi.org/10.2200/S00898ED1V01Y201902MAS023 |
| 999 |
_c562389 _d562389 |
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