Pseudoparabolic Partial Differential Equations
1970; Society for Industrial and Applied Mathematics; Volume: 1; Issue: 1 Linguagem: Inglês
10.1137/0501001
ISSN1095-7154
AutoresR. E. Showalter, Tsuan Wu Ting,
Tópico(s)Advanced Numerical Methods in Computational Mathematics
ResumoNext article Full AccessPseudoparabolic Partial Differential EquationsR. E. Showalter and T. W. TingR. E. Showalter and T. W. Tinghttps://doi.org/10.1137/0501001PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Shmuel Agmon, Lectures on elliptic boundary value problems, Prepared for publication by B. Frank Jones, Jr. with the assistance of George W. Batten, Jr. Van Nostrand Mathematical Studies, No. 2, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London, 1965v+291 MR0178246 0142.37401 Google Scholar[2] S. Agmon, , A. Douglis and , L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I, Comm. Pure Appl. Math., 12 (1959), 623–727 MR0125307 0093.10401 CrossrefISIGoogle Scholar[3] M. S. Agronovich and , M. I. Vishik, Elliptic problems with a parameter and parabolic problems of general type, Russian Math. Surveys, 19 (1964), 53–157 10.1070/rm1964v019n03ABEH001149 CrossrefGoogle Scholar[4] G. Barenblat, , I. Zheltov and , I. Kochiva, Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks, J. Appl. Math. Mech., 24 (1960), 1286–1303 10.1016/0021-8928(60)90107-6 0104.21702 CrossrefGoogle Scholar[5] G. I. Barenblatt and , G. G. Chernyi, On moment relations on surfaces of discontinuity in dissipative media, J. Appl. Math. Mech., 27 (1963), 1205–1218 10.1016/0021-8928(63)90063-7 MR0161525 0142.43304 CrossrefGoogle Scholar[6] Felix E. Browder, On the regularity properties of solutions of elliptic differential equations, Comm. Pure Appl. Math., 9 (1956), 351–361 MR0090740 0070.09601 CrossrefISIGoogle Scholar[7] Felix E. Browder, A-priori estimates for solutions of elliptic boundary-value problems. I, II, Nederl. Akad. Wetensch. Proc. Ser. A 63 = Indag. Math., 22 (1960), 145–169, 160–167 MR0123819 CrossrefGoogle Scholar[8] Felix E. Browder, On the spectral theory of elliptic differential operators. I, Math. Ann., 142 (1960/1961), 22–130 10.1007/BF01343363 MR0209909 0104.07502 CrossrefISIGoogle Scholar[9] Robert W. Carroll, Abstract methods in partial differential equations, Harper & Row Publishers, New York, 1969x+374 MR0433480 0193.06501 Google Scholar[10] R. Courant and , D. Hilbert, Methods of mathematical physics. Vol. II: Partial differential equations, (Vol. II by R. Courant.), Interscience Publishers (a division of John Wiley & Sons), New York London, 1962xxii+830 MR0140802 0099.29504 Google Scholar[11] Avner Friedman, Generalized functions and partial differential equations, Prentice-Hall Inc., Englewood Cliffs, N.J., 1963xii+340 MR0165388 0116.07002 CrossrefGoogle Scholar[12] Avner Friedman, Partial differential equations of parabolic type, Prentice-Hall Inc., Englewood Cliffs, N.J., 1964xiv+347 MR0181836 0144.34903 Google Scholar[13A] Kurt Friedrichs, Spektraltheorie halbbeschränkter Operatoren und Anwendung auf die Spektralzerlegung von Differentialoperatoren, Math. Ann., 109 (1934), 465–487 10.1007/BF01449150 MR1512905 0008.39203 CrossrefGoogle Scholar[13B] Kurt Friedrichs, Spektraltheorie halbbeschränkter Operatoren und Anwendung auf die Spektralzerlegung von Differentialoperatoren, Math. Ann., 109 (1934), 685–713 10.1007/BF01449164 MR1512919 0009.07205 CrossrefGoogle Scholar[13C] Kurt Friedrichs, Spektraltheorie halbbeschränkter Operatoren I. und II. Teil, Math. Ann., 110 (1935), 777–779 10.1007/BF01448058 MR1512969 0010.30403 CrossrefGoogle Scholar[14] K. O. Friedrichs, The identity of weak and strong extensions of differential operators, Trans. Amer. Math. Soc., 55 (1944), 132–151 MR0009701 0061.26201 CrossrefGoogle Scholar[15] S. A. Gal'pern, Cauchy problem for general systems of linear partial differential equations, Dokl. Akad. Nauk SSSR (N.S.), 119 (1958), 640–643 MR0101407 0112.32203 Google Scholar[16] I. M. Gelfand and , G. E. Shilov, Generalized Functions, Vol. 1, 2, 3, Moscow, 1958 Google Scholar[17] Günter Hellwig, Partial differential equations: An introduction, Translated by E. Gerlach, Blaisdell Publishing Co. Ginn and Co. New York-Toronto-London, 1964xiii+265 MR0173071 0133.35701 Google Scholar[18] E. Hille and , R. S. Phillips, Functional Analysis and Semigroups, Colloquium Publications, Vol. 31, American Mathematical Society, New York, 1957 0078.10004 Google Scholar[19] Eberhard Hopf, A remark on linear elliptic differential equations of second order, Proc. Amer. Math. Soc., 3 (1952), 791–793 MR0050126 0048.07802 CrossrefISIGoogle Scholar[20] Lars Hörmander, Linear partial differential operators, Die Grundlehren der mathematischen Wissenschaften, Bd. 116, Academic Press Inc., Publishers, New York, 1963vii+287 MR0161012 0108.09301 CrossrefGoogle Scholar[21] Lars Hörmander, On the theory of general partial differential operators, Acta Math., 94 (1955), 161–248 MR0076151 0067.32201 CrossrefISIGoogle Scholar[22] John Horváth, Topological vector spaces and distributions. Vol. I, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1966xii+449 MR0205028 0143.15101 Google Scholar[23] O. D. Kellog, Foundations of Potential Theory, Dover, New York, 1953 0053.07301 Google Scholar[24] A. G. Kostjučenko and , G. I. Èskin, The Cauchy problem for Sobolev-Gal' pern equations, Trudy Moskov. Mat. Obšč., 10 (1961), 273–284 MR0155094 Google Scholar[25] P. D. Lax and , A. N. Milgram, Parabolic equationsContributions to the theory of partial differential equations, Annals of Mathematics Studies, no. 33, Princeton University Press, Princeton, N. J., 1954, 167–190 MR0067317 0058.08703 Google Scholar[26] J. L. Lions, Lectures on elliptic partial differential equations, Tata Institute, Bombay, 1957 Google Scholar[27] J. L. Lions, Problèmes aux limites dans les équations aux dérivées partielles, University of Montreal, Montreal, 1962 Google Scholar[28] Norman G. Meyers and , James Serrin, $H=W$, Proc. Nat. Acad. Sci. U.S.A., 51 (1964), 1055–1056 MR0164252 0123.30501 CrossrefISIGoogle Scholar[29] Louis Nirenberg, Remarks on strongly elliptic partial differential equations, Comm. Pure Appl. Math., 8 (1955), 649–675 MR0075415 0067.07602 CrossrefISIGoogle Scholar[30] L. Nirenberg, Existence Theorems in Partial Differential Equations, New York University Press, New York, 1954 Google Scholar[31] Frigyes Riesz and , Béla Sz.-Nagy, Functional analysis, Frederick Ungar Publishing Co., New York, 1955xii+468 MR0071727 Google Scholar[32] G. E. Shilov, Correct boundary value problems in a half-space for linear partial differential equations with constant coefficients, Russian Math. Surveys, 19 (1964), 1–52 10.1070/rm1964v019n03ABEH001148 0132.07401 CrossrefGoogle Scholar[33] S. Sobolev, On a theorem of functional analysis, Math. Sbornik, 4 (1938), 471–497 Google Scholar[34] S. Sobolev, Some new problems in mathematical physics, Izv. Akad. Nauk SSSR Ser. Mat., 18 (1954), 3–50 Google Scholar[35] D. W. Taylor, Research on Consolidation of Clays, Massachusetts Institute of Technology Press, Cambridge, 1942 Google Scholar[36] Tsuan Wu Ting, Certain non-steady flows of second-order fluids, Arch. Rational Mech. Anal., 14 (1963), 1–26 10.1007/BF00250690 MR0153255 0139.20105 CrossrefISIGoogle Scholar[37] Tsuan Wu Ting, Parabolic and pseudo-parabolic partial differential equations, J. Math. Soc. Japan, 21 (1969), 440–453 MR0264231 0177.36701 CrossrefISIGoogle Scholar[38] C. Truesdell and , W. Noll, The non-linear field theories of mechanicsEncyclopedia of Physics, vol. III, Springer-Verlag, Berlin, 1965 CrossrefGoogle Scholar[39] Kôsaku Yosida, On the differentiability and the representation of one-parameter semi-group of linear operators, J. Math. Soc. Japan, 1 (1948), 15–21 MR0028537 0037.35302 CrossrefGoogle Scholar[40] Kôsaku Yosida, Functional analysis, Die Grundlehren der Mathematischen Wissenschaften, Band 123, Academic Press Inc., New York, 1965xi+458 MR0180824 0126.11504 CrossrefGoogle Scholar[41] T. Zalenyak, The behavior for $t\rightarrow\infty$ of solutions of a problem of S. L. Sobolev, Soviet Math. Dokl., 2 (1961), 956–958 0128.32703 Google Scholar[42] T. Zalenyak, A problem of Sobolev, Soviet Math. Dokl., 3 (1962), 1756–1759 0163.33301 Google Scholar Next article FiguresRelatedReferencesCited ByDetails On the critical behavior for time-fractional pseudo-parabolic-type equations with combined nonlinearitiesBoundary Value Problems, Vol. 2022, No. 1 | 4 April 2022 Cross Ref Two approximation methods for fractional order Pseudo-Parabolic differential equationsAlexandria Engineering Journal, Vol. 61, No. 12 | 1 Dec 2022 Cross Ref On a system of nonlinear pseudoparabolic equations with Robin-Dirichlet boundary conditionsCommunications on Pure & Applied Analysis, Vol. 21, No. 2 | 1 Jan 2022 Cross Ref On time fractional pseudo-parabolic equations with nonlocal integral conditionsEvolution Equations & Control Theory, Vol. 11, No. 1 | 1 Jan 2022 Cross Ref Boundary value problem with a displacement for a hyperbolic equation of third order with a derivative under boundary conditionsВестник КРАУНЦ. 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