# On the asymptotic behavior of solutions of linear parabolic equations in ${L}^{1}$ space

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1987)

- Volume: 14, Issue: 4, page 587-611
- ISSN: 0391-173X

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topPark, Dong Gun, and 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 14.4 (1987): 587-611. <http://eudml.org/doc/84019>.

@article{Park1987,

author = {Park, Dong Gun, Tanabe, Hiroki},

journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},

keywords = {asymptotic behavior; initial-boundary value problem; asymptotic expansion; Green function estimates; real interpolation},

language = {eng},

number = {4},

pages = {587-611},

publisher = {Scuola normale superiore},

title = {On the asymptotic behavior of solutions of linear parabolic equations in $L^1$ space},

url = {http://eudml.org/doc/84019},

volume = {14},

year = {1987},

}

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

PB - Scuola normale superiore

VL - 14

IS - 4

SP - 587

EP - 611

LA - eng

KW - asymptotic behavior; initial-boundary value problem; asymptotic expansion; Green function estimates; real interpolation

UR - http://eudml.org/doc/84019

ER -

## References

top- [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. Zbl0195.11401MR274983
- [2] F.E. Browder, On the spectral theory of elliptic operators. I, Math. Ann., 142 (1961), pp. 22-130. Zbl0104.07502MR209909
- [3] P. Grisvard, Équations differentielles abstraites, Ann. Scient. Ecole Norm. Sup., 2 (1969), pp. 311-195. Zbl0193.43502MR270209
- [4] D. Guidetti, On the asymptotic behavior of solutions of linear nonautonomous parabolic equations, preprint. Zbl0637.35042MR923439
- [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. MR257589
- [6] D.G. Park, Initial-boundary value problem for parabolic equation in L1, Proc. Japan Acad., 62 (1986), pp. 178-180. Zbl0668.35042MR854213
- [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. Zbl0655.35031MR927065
- [8] A. Pazy, Asymptotic behavior of the solution of an abstract evolution equation and some applications, J. Diff. Eq., 4 (1968), pp. 493-509. Zbl0174.13802MR233095
- [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. Zbl0123.10402MR131041
- [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).

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