Parabolic and pseudo-parabolic partial differential equations

Tsuan Wu TING

doi:10.2969/jmsj/02130440

Tsuan Wu TING

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1969 Volume 21 Issue 3 Pages 440-453

DOI https://doi.org/10.2969/jmsj/02130440

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Published: 1969 Received: June 13, 1967 Available on J-STAGE: September 29, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: September 29, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) K. Yosida, Functional analysis, Springer, Berlin, 1965, Chaps. IX, XIV.
2) L. Nirenberg, On elliptic partial differential equations, Ann. Scuola Norm. Sup. Pisa, Ser. 3, 13 (1959), 115-162.
3) A. Friedman, Partial differential equations of parabolic type, Prentice-Hall, N.J., 1964, Chap. 10.
4) P.D. Lax and A.N. Milgram, Parabolic equations, Contributions to the theory of partial differential equations, Ann. Math. Studies, No. 33, Princeton Univ. Press, 1954, pp. 167-190.
5) K. Yosida, On the differentiability and the representation of one-parameter semi-groups of linear operators, J. Math. Soc. Japan, 1 (1948), 15-21.
6) C. Truesdell and W. Noll, The non-linear field theories of mechanics, Encyclopedia of Physics, Vol. III/3, Springer, Berlin, 1965.
7) T. W. Ting, Certain non-steady flows of second-order fluids, Arch. Rational Mech. Anal., 14 (1963), 1-26.
8) G. I. Barenblat, Iu, P. Zheltov and I. N. Kochina, Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks, J. Appl. Math. Mech. (ASME Translations of PMM), 24 (1960), 1286-1303.
9) G. I. Barenblat and G. G. Chernyi, On moment relations on surface of discontinuityin dissipative media, J. Appl. Math. Mech. (ASME Translations), 27 (1963), 1205-1218.
10) R. E. Showalter and T. W. Ting, Pseudo-parabolic partial differential equations, SIAM J. Appl. Math. (to appear).
11) A. Friedman, Interior estimates for parabolic system of partial differential equations, J. Math. Mech., 7 (1958), 393-418.
12) E. Hille and R. S. Phillips, Functional analysis and semi-groups, Colloq. Publ. Amer. Math. Soc., 1957, Chap. XII.
13) A. V. Balarkrishnan, Fractional powers of closed operators and the semi-groups generated by them, Pacific J. Math., 10 (1960), 419-437.
14) T. Kato, Fractional powers of dissipative operators, J. Math. Soc. Japan, 13 (1961), 246-274; II, J. Math. Soc. Japan, 14 (1962), 242-248.
15) J. L. Lions, Espaces d'interpolation et domaines de puissances fractionnaires d'operateurs, J. Math. Soc. Japan, 14 (1962), 233-241.
16) 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.
17) F. E. Browder, On the regularity properties of solutions of elliptic differential equations, Comm. Pure Appl. Math., 9 (1956), 351-361.
18) S. Agmon, The L_p approach to the Dirichlet problem, Ann. Scuola Norm. Sup. Pisa, Ser. 3, 13 (1959), 405-448.

Right : [1] K. Yosida, Functional analysis, Springer, Berlin, 1965, Chaps. IX, XIV.
[2] L. Nirenberg, On elliptic partial differential equations, Ann. Scuola Norm. Sup. Pisa, Ser. 3, 13 (1959), 115-162.
[3] A. Friedman, Partial differential equations of parabolic type, Prentice-Hall, N. J., 1964, Chap. 10.
[4] P. D. Lax and A. N. Milgram, Parabolic equations, Contributions to the theory of partial differential equations, Ann. Math. Studies, No. 33, Princeton Univ. Press, 1954, pp. 167-190.
[5] K. Yosida, On the differentiability and the representation of one-parameter semigroups of linear operators, J. Math. Soc. Japan, 1 (1948), 15-21.
[6] C. Truesdell and W. Noll, The non-linear field theories of mechanics, Encyclopedia of Physics, Vol. III/3, Springer, Berlin, 1965.
[7] T. W. Ting, Certain non-steady flows of second-order fluids, Arch. Rational Mech. Anal., 14 (1963), 1-26.
[8] G. I. Barenblat, Iu, P. Zheltov and I. N. Kochina, Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks, J. Appl. Math. Mech. (ASME Translations of PMM), 24 (1960), 1286-1303.
[9] G. I. Barenblat and G. G. Chernyi, On moment relations on surface of discontinuity in dissipative media, J. Appl. Math. Mech. (ASME Translations), 27 (1963), 1205-1218.
[10] R. E. Showalter and T. W. Ting, Pseudo-parabolic partial differential equations, SIAM J. Appl. Math. (to appear).
[11] A. Friedman, Interior estimates for parabolic system of partial differential equations, J. Math. Mech., 7 (1958), 393-418.
[12] E. Hille and R. S. Phillips, Functional analysis and semi-groups, Colloq. Publ. Amer. Math. Soc., 1957, Chap. XII.
[13] A. V. Balarkrishnan, Fractional powers of closed operators and the semi-groups generated by them, Pacific J. Math., 10 (1960), 419-437.
[14] T. Kato, Fractional powers of dissipative operators, J. Math. Soc. Japan, 13 (1961), 246-274; II, J. Math. Soc. Japan, 14 (1962), 242-248.
[15] J. L. Lions, Espaces d'interpolation et domaines de puissances fractionnaires d'operateurs, J. Math. Soc. Japan, 14 (1962), 233-241.
[16] 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.
[17] F. E. Browder, On the regularity properties of solutions of elliptic differential equations, Comm. Pure Appl. Math., 9 (1956), 351-361.
[18] S. Agmon, The L_p approach to the Dirichlet problem, Ann. Scuola Norm. Sup. Pisa, Ser. 3, 13 (1959), 405-448.

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