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## Annales Polonici Mathematici

1996 | 63 | 3 | 223-234
Tytuł artykułu

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

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We consider the second order parabolic partial differential equation
$∑^n_{i,j=1} a_{ij}(x,t) u_{x_{i}x_{j}} + ∑^n_{i=1} b_i(x,t) u_{x_i} + c(x,t)u - u_t = 0$.
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
$L^α[u^α] + ∑_{β=1}^N c^{αβ}(x,t) u^β = f^α(x,t)$,
where
$L^α[u] ≡ ∑^n_{i,j=1} a_{ij}^α(x,t) u_{x_{i}x_{j}} + ∑^n_{i=1} b_i^α(x,t) u_{x_i} - u_t$,
must decay as t → ∞.
Słowa kluczowe
EN
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
223-234
Opis fizyczny
Daty
wydano
1996
otrzymano
1994-06-16
poprawiono
1995-08-31
Twórcy
autor
• Department of Mathematics, National Central University, Chung-Li, 32054 Taiwan, Republic of China
autor
• Department of Mathematics, National Central University, Chung-Li, 32054 Taiwan, Republic of China
Bibliografia
• [1] P. J. Chabrowski, Propriétés asymptotiques d'une mesure associée à l'équation différentielle aux dérivées partielles de type parabolique, Funkc. Ekvac. 13 (1970), 35-43.
• [2] L. S. Chen, On the behavior of solutions for large |x| of parabolic equations with unbounded coefficients, Tôhoku Math. J. 20 (1968), 589-595.
• [3] L. S. Chen, Note on the behavior of solutions of parabolic equations with unbounded coefficients, Nagoya Math. J. 37 (1970), 1-4.
• [4] L. S. Chen, Remark on behavior of solutions of some parabolic equations, Tôhoku Math. J. 22 (1970), 511-516.
• [5] L. S. Chen, J. S. Lin and C. C. Yeh, Asymptotic behavior of solutions for large |x| of weakly coupled parabolic systems with unbounded coefficients, Hiroshima Math. J. 4 (1974), 477-490.
• [6] L. S. Chen, C. C. Yeh and H. Y. Chen, On the behavior of solutions of the Cauchy problem for parabolic equations with unbounded coefficients, Hiroshima Math. J. 1 (1971), 145-153.
• [7] C. Cosner, A Phragmén-Lindelöf principle and asymptotic behavior for weakly coupled systems of parabolic equations with unbounded coefficients, Dissertation, University of California, Berkeley, 1977.
• [8] C. Cosner, Asymptotic behavior of solutions of second order parabolic partial differentical equations with unbounded coefficients, J. Differential Equations 35 (1980), 407-428.
• [9] S. D. Èĭdel'man and F. O. Porper, Properties of solutions of second-order parabolic equations with dissipation, Differential Equations 7 (1971), 1280-1288.
• [10] S. D. Èĭdel'man and F. O. Porper, On the asymptotic behavior of solutions of parabolic systems with dissipation, Soviet Math. Dokl. 12 (1971), 471-475.
• [11] M. Krzyżański, Evaluations des solutions de l'équation linéaire de type parabolique à coefficients non bornés, Ann. Polon. Math. 11 (1962), 253-260.
• [12] T. Kuroda, Asymptotic behavior of solutions of parabolic equations with unbounded coefficients, Nagoya Math. J. 37 (1970), 5-12.
• [13] T. Kuroda and L. S. Chen, On the behavior of solutions of parabolic equations with unbounded coefficients, Ann. Polon. Math. 23 (1970), 57-64.
• [14] T. Kusano, On the decay for large |x| of solutions of parabolic equations with unbounded coefficients, Publ. Res. Inst. Math. Sci. Kyoto Univ. Ser. A 3 (1967), 203-210.
• [15] T. Kusano, On the behavior of large |x| for solutions of parabolic equations with unbounded coefficients, Funkc. Ekvac. 11 (1968), 169-174.
• [16] T. Kusano, T. Kuroda and L. S. Chen, Weakly coupled parabolic systems with unbounded coefficients, Hiroshima Math. J. 3 (1973), 1-14.
• [17] T. Kusano, T. Kuroda and L. S. Chen, Some parabolic equations with unbounded coefficients, Funkc. Ekvac. 16 (1973), 1-28.
• [18] M. H. Protter and H. F. Weinberger, Maximum Principles in Differential Equations, Prentice-Hall, Englewood Cliffs, N.J., 1967.
Typ dokumentu
Bibliografia
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