TY - JOUR
T1 - Asymptotic behaviors of solutions to evolution equations in the presence of translation and scaling invariance
AU - Kagei, Yoshiyuki
AU - Maekawa, Yasunori
PY - 2011/5/15
Y1 - 2011/5/15
N2 - There are wide classes of nonlinear evolution equations which possess invariant properties with respect to a scaling and translations. If a solution is invariant under the scaling then it is called a self-similar solution, which is a candidate for the asymptotic profile of general solutions at large time. In this paper we establish an abstract framework to find more precise asymptotic profiles by shifting self-similar solutions suitably.
AB - There are wide classes of nonlinear evolution equations which possess invariant properties with respect to a scaling and translations. If a solution is invariant under the scaling then it is called a self-similar solution, which is a candidate for the asymptotic profile of general solutions at large time. In this paper we establish an abstract framework to find more precise asymptotic profiles by shifting self-similar solutions suitably.
KW - Evolution equations
KW - Large time behaviors of solutions
KW - Self-similar solutions
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U2 - 10.1016/j.jfa.2011.02.004
DO - 10.1016/j.jfa.2011.02.004
M3 - Article
AN - SCOPUS:79952102369
VL - 260
SP - 3036
EP - 3096
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
SN - 0022-1236
IS - 10
ER -