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

• Autorzy: Wei-Cheng Lian , Cheh-Chih Yeh
• 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

asymptotic behavior; second order partial differential equation; maximum principles

Kategorie tematyczne

• 35K40: Second-order parabolic systems
• 35B40: Asymptotic behavior of solutions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1996
• Tom: 63
• Numer: 3
• Strony: 223-234

Daty

wydano

1996

otrzymano

1994-06-16

poprawiono

1995-08-31

Twórcy

autor

Wei-Cheng Lian

• Department of Mathematics, National Central University, Chung-Li, 32054 Taiwan, Republic of China

autor

Cheh-Chih Yeh

• Department of Mathematics, National Central University, Chung-Li, 32054 Taiwan, Republic of China

Bibliografia

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