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

Annales Polonici Mathematici (1996)

- Volume: 63, Issue: 3, page 223-234
- ISSN: 0066-2216

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topWei-Cheng Lian, and Cheh-Chih Yeh. "On the asymptotic behavior of solutions of second order parabolic partial differential equations." Annales Polonici Mathematici 63.3 (1996): 223-234. <http://eudml.org/doc/262828>.

@article{Wei1996,

abstract = {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 → ∞.},

author = {Wei-Cheng Lian, Cheh-Chih Yeh},

journal = {Annales Polonici Mathematici},

keywords = {asymptotic behavior; second order partial differential equation; maximum principles; large time behaviour},

language = {eng},

number = {3},

pages = {223-234},

title = {On the asymptotic behavior of solutions of second order parabolic partial differential equations},

url = {http://eudml.org/doc/262828},

volume = {63},

year = {1996},

}

TY - JOUR

AU - Wei-Cheng Lian

AU - Cheh-Chih Yeh

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

JO - Annales Polonici Mathematici

PY - 1996

VL - 63

IS - 3

SP - 223

EP - 234

AB - 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 → ∞.

LA - eng

KW - asymptotic behavior; second order partial differential equation; maximum principles; large time behaviour

UR - http://eudml.org/doc/262828

ER -

## References

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