TY - JOUR
T1 - Global existence, large time behavior and life span of solutions of a semilinear parabolic cauchy problem
AU - Lee, Tzong Yow
AU - Ni, Wei Ming
N1 - Copyright:
Copyright 2016 Elsevier B.V., All rights reserved.
PY - 1992/9
Y1 - 1992/9
N2 - We investigate the behavior of the solution u(x, t) of (equation formula) is the Laplace operator, p > 1 is a constant, T > 0, and φ is a nonnegative bounded continuous function in ℝn. The main results are for the case when the initial value φ has polynomial decay near x = ∞. Assuming φ φ λ(l + |x|) n with λ, a > 0, various questions of global (in time) existence and nonexistence, arge time behavior or life span of the solution u(x, i) are answered in terms of simple conditions on X, a, p and the space dimension n.
AB - We investigate the behavior of the solution u(x, t) of (equation formula) is the Laplace operator, p > 1 is a constant, T > 0, and φ is a nonnegative bounded continuous function in ℝn. The main results are for the case when the initial value φ has polynomial decay near x = ∞. Assuming φ φ λ(l + |x|) n with λ, a > 0, various questions of global (in time) existence and nonexistence, arge time behavior or life span of the solution u(x, i) are answered in terms of simple conditions on X, a, p and the space dimension n.
KW - Global existence
KW - Large time asymptotic behaviors
KW - Life span
KW - Semilinear parabolic Cauchy problem
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U2 - 10.1090/S0002-9947-1992-1057781-6
DO - 10.1090/S0002-9947-1992-1057781-6
M3 - Article
AN - SCOPUS:84968508643
VL - 333
SP - 365
EP - 378
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
SN - 0002-9947
IS - 1
ER -