On the asymptotic behavior of solutions of linear parabolic equations in L 1 space
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 14 (1987) no. 4, pp. 587-611.
@article{ASNSP_1987_4_14_4_587_0,
     author = {Park, Dong Gun and Tanabe, Hiroki},
     title = {On the asymptotic behavior of solutions of linear parabolic equations in $L^1$ space},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {587--611},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 14},
     number = {4},
     year = {1987},
     mrnumber = {963491},
     zbl = {0676.35036},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1987_4_14_4_587_0/}
}
TY  - JOUR
AU  - Park, Dong Gun
AU  - Tanabe, Hiroki
TI  - On the asymptotic behavior of solutions of linear parabolic equations in $L^1$ space
JO  - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY  - 1987
SP  - 587
EP  - 611
VL  - 14
IS  - 4
PB  - Scuola normale superiore
UR  - http://www.numdam.org/item/ASNSP_1987_4_14_4_587_0/
LA  - en
ID  - ASNSP_1987_4_14_4_587_0
ER  - 
%0 Journal Article
%A Park, Dong Gun
%A Tanabe, Hiroki
%T On the asymptotic behavior of solutions of linear parabolic equations in $L^1$ space
%J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
%D 1987
%P 587-611
%V 14
%N 4
%I Scuola normale superiore
%U http://www.numdam.org/item/ASNSP_1987_4_14_4_587_0/
%G en
%F ASNSP_1987_4_14_4_587_0
Park, Dong Gun; Tanabe, Hiroki. On the asymptotic behavior of solutions of linear parabolic equations in $L^1$ space. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 14 (1987) no. 4, pp. 587-611. http://www.numdam.org/item/ASNSP_1987_4_14_4_587_0/

[1] R. Beals, Asymptotic behavior of the Green's function and spectral function of an elliptic operator, J. Func. Anal., 5 (1970), pp. 484-503. | MR | Zbl

[2] F.E. Browder, On the spectral theory of elliptic operators. I, Math. Ann., 142 (1961), pp. 22-130. | MR | Zbl

[3] P. Grisvard, Équations differentielles abstraites, Ann. Scient. Ecole Norm. Sup., 2 (1969), pp. 311-195. | Numdam | MR | Zbl

[4] D. Guidetti, On the asymptotic behavior of solutions of linear nonautonomous parabolic equations, preprint. | MR

[5] L. Hörmander, On the Riesz means of spectral functions and eigenfunction expansions for elliptic differential operators, Some Recent Advances in the Basic Sciences, 2 (Proc. Annual. Sci. Conf., Belfer Grad. School Sci., Yeshiva Univ., New York, 1965- 1966), pp. 155-202. | MR

[6] D.G. Park, Initial-boundary value problem for parabolic equation in L1, Proc. Japan Acad., 62 (1986), pp. 178-180. | MR | Zbl

[7] D.G. Park, Regularity in time of the solution of parabolic initial-boundary value problem in L1 space, Osaka J. Math., 24 (1987), pp. 911-930. | MR | Zbl

[8] A. Pazy, Asymptotic behavior of the solution of an abstract evolution equation and some applications, J. Diff. Eq., 4 (1968), pp. 493-509. | MR | Zbl

[9] H. Tanabe, Convergence to a stationary state of the solution of some kinds of differential equations in a Banach space, Proc. Japan Acad., 37 (1961), pp. 127-130. | MR | Zbl

[10] H. Tanabe, On semilinear equations of elliptic and parabolic type, Functional Analysis and Numerical Analysis, Japan-France Seminar, Tokyo and Kyoto, 1967 (ed. H. Fujita), Japan Society for the Promotion of Science, 1978, pp. 455-463.

[11] H. Tanabe, Functional Analysis. II, Jikkyo Shuppan Publishing Company, Tokyo, 1981 (in Japanese).