TY - JOUR
T1 - Heat equation with a nonlinear boundary condition and growing initial data
AU - Ishige, Kazuhiro
AU - Sato, Ryuichi
N1 - Funding Information:
for all sufficiently large κ. Thus Corollary 1.3 follows. □ Acknowledgements. The authors would like to thank the referees for their valuable comments. The first author was supported in part by the Grant-in-Aid for Scientific Research (A)(No. 15H02058), from Japan Society for the Promotion of Science. The second author was supported in part by Research Fellow of Japan Society for the Promotion of Science.
PY - 2017/7/1
Y1 - 2017/7/1
N2 - We discuss the solvability and the comparison principle for the heat equation with a nonlinear boundary condition ∂tu = Δ x ∈ Ω t > 0; ∇u .v(x) = up; x ∈ ∂ Δ t > 0;(x; 0) ∝ = (x) x ∈ Ω where N ≥ 1, p > 1, is a smooth domain in RN and '(x) = O(eλd(x)2 ) as d(x) → 1 for some λ ≥ 0. Here, d(x) = dist (x; ∈ Ω). Furthermore, we obtain the lower estimates of the blow-up time of solutions with large initial data by use of the behavior of the initial data near the boundary ∈ Ω.
AB - We discuss the solvability and the comparison principle for the heat equation with a nonlinear boundary condition ∂tu = Δ x ∈ Ω t > 0; ∇u .v(x) = up; x ∈ ∂ Δ t > 0;(x; 0) ∝ = (x) x ∈ Ω where N ≥ 1, p > 1, is a smooth domain in RN and '(x) = O(eλd(x)2 ) as d(x) → 1 for some λ ≥ 0. Here, d(x) = dist (x; ∈ Ω). Furthermore, we obtain the lower estimates of the blow-up time of solutions with large initial data by use of the behavior of the initial data near the boundary ∈ Ω.
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M3 - Article
AN - SCOPUS:85028703481
VL - 30
SP - 481
EP - 504
JO - Differential and Integral Equations
JF - Differential and Integral Equations
SN - 0893-4983
IS - 7-8
ER -