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Algebra i Analiz, 2003, Volume 15, Issue 1, Pages 201–214 (Mi aa776)  

This article is cited in 24 scientific papers (total in 24 papers)

Research Papers

Backward uniqueness for the heat operator in half-space

L. Escauriazaa, G. Sereginb, V. Šverakc

a Dipartimento di Matematicas, UPV/EHU, Bilbao, Spain
b С.-Петербургское отделение Математического института им. В. А. Стеклова РАН, Санкт-Петербург, Россия
c School of Mathematics, University of Minnesota, Minneapolis, USA

Abstract: A backward uniqueness result is proved for the heat operator with variable lower order terms in a half-space. The main point of the result is that the boundary conditions are not controlled by the assumptions.

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Received: 02.09.2002
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Citation: L. Escauriaza, G. Seregin, V. Šverak, “Backward uniqueness for the heat operator in half-space”, Algebra i Analiz, 15:1 (2003), 201–214

Citation in format AMSBIB
\Bibitem{EscSerSve03}
\by L.~Escauriaza, G.~Seregin, V.~{\v S}verak
\paper Backward uniqueness for the heat operator in half-space
\jour Algebra i Analiz
\yr 2003
\vol 15
\issue 1
\pages 201--214
\mathnet{http://mi.mathnet.ru/aa776}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1979722}
\zmath{https://zbmath.org/?q=an:1053.35052}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. L. Escauriaza, G. A. Seregin, V. Šverak, “$L_{3,\infty}$-solutions of the Navier–Stokes equations and backward uniqueness”, Russian Math. Surveys, 58:2 (2003), 211–250  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. J. Math. Sci. (N. Y.), 130:4 (2005), 4884–4892  mathnet  crossref  mathscinet  zmath
    3. Seregin G, “On smoothness of $L_{3,\infty}$-infinity-solutions to the Navier–Stokes equations up to boundary”, Math. Ann., 332:1 (2005), 219–238  crossref  mathscinet  zmath  isi  elib  scopus
    4. G. A. Seregin, “New version of the Ladyzhenskaya–Prodi–Serrin condition”, St. Petersburg Math. J., 18:1 (2007), 89–103  mathnet  crossref  mathscinet  zmath  elib
    5. J. Math. Sci. (N. Y.), 143:2 (2007), 2924–2935  mathnet  crossref  mathscinet  zmath  elib
    6. Escauriaza L., Kenig C. E., Ponce G., Vega L., “Decay at infinity of caloric functions within characteristic hyperplanes”, Math. Res. Lett., 13:2-3 (2006), 441–453  crossref  mathscinet  zmath  isi  elib
    7. Martinez P., Vancostenoble J., “Carleman estimates for one-dimensional degenerate heat equations”, J. Evol. Equ., 6:2 (2006), 325–362  crossref  mathscinet  zmath  isi  elib  scopus
    8. Seregin G., Zajaczkowski W., “A sufficient condition of regularity for axially symmetric solutions to the Navier–Stokes equations”, SIAM J. Math. Anal., 39:2 (2007), 669–685 (electronic)  crossref  mathscinet  zmath  isi  elib  scopus
    9. Vessella S., “Quantitative estimates of unique continuation for parabolic equations, determination of unknown time-varying boundaries and optimal stability estimates”, Inverse Problems, 24:2 (2008), 023001, 81 pp.  crossref  mathscinet  zmath  adsnasa  isi  scopus
    10. Cannarsa P., Martinez P., Vancostenoble J., “Carleman estimates for a class of degenerate parabolic operators”, SIAM J. Control Optim., 47:1 (2008), 1–19  crossref  mathscinet  zmath  isi  elib  scopus
    11. Cannarsa P., Martinez P., Vancostenoble J., “Carleman estimates and null controllability for boundary-degenerate parabolic operators”, C. R. Math. Acad. Sci. Paris, 347:3–4 (2009), 147  crossref  mathscinet  zmath  isi  scopus
    12. J. Math. Sci. (N. Y.), 166:1 (2010), 40–52  mathnet  crossref
    13. Kang K., Lee J., “Interior regularity criteria for suitable weak solutions of the magnetohydrodynamic equations”, Journal of Differential Equations, 247:8 (2009), 2310–2330  crossref  mathscinet  zmath  adsnasa  isi  scopus
    14. Du D., Lue J., “Blow–up for a semi–linear advection–diffusion system with energy conservation”, Chinese Annals of Mathematics Series B, 30:4 (2009), 433–446  crossref  mathscinet  zmath  isi  scopus
    15. Yamamoto M., “Carleman estimates for parabolic equations and applications”, Inverse Problems, 25:12 (2009), 123013  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    16. J. Math. Sci. (N. Y.), 178:3 (2011), 282–291  mathnet  crossref
    17. Nguyen T.A., “On a Question of Landis and Oleinik”, Transactions of the American Mathematical Society, 362:6 (2010), 2875–2899  crossref  mathscinet  zmath  isi  scopus
    18. Kang K., Kim J.-M., “Regularity Criteria of the Magnetohydrodynamic Equations in Bounded Domains Or a Half Space”, J. Differ. Equ., 253:2 (2012), 764–794  crossref  mathscinet  zmath  adsnasa  isi  scopus
    19. Wu J., Wang W., “On Backward Uniqueness For the Heat Operator in Cones”, J. Differ. Equ., 258:1 (2015), 224–241  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    20. Wu J., Zhang L., “Backward Uniqueness For Parabolic Operators With Variable Coefficients in a Half Space”, Commun. Contemp. Math., 18:1 (2016), 1550011  crossref  mathscinet  zmath  isi  elib  scopus
    21. Wang L., “Uniqueness of self-similar shrinkers with asymptotically cylindrical ends”, J. Reine Angew. Math., 715 (2016), 207–230  crossref  mathscinet  zmath  isi  elib  scopus
    22. Cannarsa P., Martinez P., Vancostenoble J., “Global Carleman Estimates For Degenerate Parabolic Operators With Applications Introduction”, Mem. Am. Math. Soc., 239:1133 (2016), 1+  crossref  mathscinet  isi  elib
    23. Araruna F.D., Araujo B.S.V., Fernandez-Cara E., “Stackelberg-Nash Null Controllability For Some Linear and Semilinear Degenerate Parabolic Equations”, Math. Control Signal Syst., 30:3 (2018), 14  crossref  mathscinet  isi  scopus
    24. Kim J.-M., “Regularity Criteria For Weak Solutions to the 3D Navier-Stokes Equations in Bounded Domains Via Bmo Norm”, Electron. J. Differ. Equ., 2019, 07  mathscinet  zmath  isi
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