Geodesic
Lower Bounds for Solutions of Parabolic Differential Inequalities
Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 667-672

Voir la notice de l'article provenant de la source Cambridge University Press

Let P be the parabolic differential operator where E is a linear elliptic operator of second order on D × [0, ∞), D being a bounded domain in Rn . The asymptotic behaviour of solutions u(x, t) of differential inequalities of the form 1 has been investigated by Protter (4). He found conditions on the functions ƒ and g under which solutions of (1), vanishing on the boundary of D and tending to zero with sufficient rapidity as t → ∞, vanish identically for all t ⩾ 0. Similar results have been found by Lees (1) for parabolic differential inequalities in Hilbert space. 
Ogawa, Hajimu. Lower Bounds for Solutions of Parabolic Differential Inequalities. Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 667-672. doi: 10.4153/CJM-1967-061-9
@article{10_4153_CJM_1967_061_9,
     author = {Ogawa, Hajimu},
     title = {Lower {Bounds} for {Solutions} of {Parabolic} {Differential} {Inequalities}},
     journal = {Canadian journal of mathematics},
     pages = {667--672},
     year = {1967},
     volume = {19},
     number = {1},
     doi = {10.4153/CJM-1967-061-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1967-061-9/}
}
TY  - JOUR
AU  - Ogawa, Hajimu
TI  - Lower Bounds for Solutions of Parabolic Differential Inequalities
JO  - Canadian journal of mathematics
PY  - 1967
SP  - 667
EP  - 672
VL  - 19
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1967-061-9/
DO  - 10.4153/CJM-1967-061-9
ID  - 10_4153_CJM_1967_061_9
ER  - 
%0 Journal Article
%A Ogawa, Hajimu
%T Lower Bounds for Solutions of Parabolic Differential Inequalities
%J Canadian journal of mathematics
%D 1967
%P 667-672
%V 19
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1967-061-9/
%R 10.4153/CJM-1967-061-9
%F 10_4153_CJM_1967_061_9

[1] 1. Lees, M., Asymptotic behaviour of solutions of parabolic differential inequalities, Can. J. Math., 14 (1962), 626–631. Google Scholar

[2] 2. Lions, J. L. and Malgrange, B., Sur l'unicité rétrograde dans les problèmes mixtes paraboliques, Math. Scand., 8 (1960), 277–286. Google Scholar

[3] 3. Ogawa, H., Lower bounds for solutions of differential inequalities in Hilbert space, Proc. Amer. Math. Soc., 16 (1965), 1241–1243. Google Scholar

[4] 4. Protter, M. H., Properties of solutions of parabolic equations and inequalities, Can. J. Math., 13 (1961), 331–345. Google Scholar

Cité par Sources :