On the asymptotic behavior of solutions of second order parabolic partial differential equations

Wei-Cheng Lian; Cheh-Chih Yeh

Annales Polonici Mathematici, Tome 63 (1996), p. 223-234 / Harvested from The Polish Digital Mathematics Library

Résumé

We consider the second order parabolic partial differential equation $\sum_{i, j = 1}^{n} a_{i j} (x, t) u_{x_{i} x_{j}} + \sum_{i = 1}^{n} b_{i} (x, t) u_{x_{i}} + c (x, t) u - u_{t} = 0$ . Sufficient conditions are given under which every solution of the above equation must decay or tend to infinity as |x|→ ∞. A sufficient condition is also given under which every solution of a system of the form $L^{α} [u^{α}] + \sum_{β = 1}^{N} c^{α β} (x, t) u^{β} = f^{α} (x, t)$ , where $L^{α} [u] \equiv \sum_{i, j = 1}^{n} a_{i j}^{α} (x, t) u_{x_{i} x_{j}} + \sum_{i = 1}^{n} b_{i}^{α} (x, t) u_{x_{i}} - u_{t}$ , must decay as t → ∞.

Publié le : 1996-01-01

Zbl 0851.35019

EUDML-ID : urn:eudml:doc:262828

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     author = {Wei-Cheng Lian and Cheh-Chih Yeh},
     title = {On the asymptotic behavior of solutions of second order parabolic partial differential equations},
     journal = {Annales Polonici Mathematici},
     volume = {63},
     year = {1996},
     pages = {223-234},
     zbl = {0851.35019},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv63z3p223bwm}
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Wei-Cheng Lian; Cheh-Chih Yeh. On the asymptotic behavior of solutions of second order parabolic partial differential equations. Annales Polonici Mathematici, Tome 63 (1996) pp. 223-234. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv63z3p223bwm/

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