TY - JOUR
T1 - Supersolutions for a class of nonlinear parabolic systems
AU - Ishige, Kazuhiro
AU - Kawakami, Tatsuki
AU - Sierzȩga, Mikołaj
N1 - Funding Information:
The first author was supported by the Grant-in-Aid for Scientific Research (A) (No. 15H02058 ), from Japan Society for the Promotion of Science . The second author was supported by the Grant-in-Aid for Young Scientists (B) (No. 24740107 ) from Japan Society for the Promotion of Science and by the JSPS Program for Advancing Strategic International Networks to Accelerate the Circulation of Talented Researchers “Mathematical Science of Symmetry, Topology and Moduli, Evolution of International Research Network based on OCAMI”. The third author was partially supported by WCMCS , Warsaw.
Publisher Copyright:
© 2015 Elsevier Inc.
PY - 2016/4/5
Y1 - 2016/4/5
N2 - In this paper, by using scalar nonlinear parabolic equations, we construct supersolutions for a class of nonlinear parabolic systems including{∂tu=δu+vp,x∈Ω,t>0,∂tv=δv+uq,x∈Ω,t>0,u=v=0,x∈∂Ω,t>0,(u(x,0),v(x,0))=(u0(x),v0(x)),x∈Ω, where p≥0, q≥0, Ω is a (possibly unbounded) smooth domain in RN and both u0 and v0 are nonnegative and locally integrable functions in Ω. The supersolutions enable us to obtain optimal sufficient conditions for the existence of the solutions and optimal lower estimates of blow-up rate of the solutions.
AB - In this paper, by using scalar nonlinear parabolic equations, we construct supersolutions for a class of nonlinear parabolic systems including{∂tu=δu+vp,x∈Ω,t>0,∂tv=δv+uq,x∈Ω,t>0,u=v=0,x∈∂Ω,t>0,(u(x,0),v(x,0))=(u0(x),v0(x)),x∈Ω, where p≥0, q≥0, Ω is a (possibly unbounded) smooth domain in RN and both u0 and v0 are nonnegative and locally integrable functions in Ω. The supersolutions enable us to obtain optimal sufficient conditions for the existence of the solutions and optimal lower estimates of blow-up rate of the solutions.
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U2 - 10.1016/j.jde.2015.12.031
DO - 10.1016/j.jde.2015.12.031
M3 - Article
AN - SCOPUS:84958213141
VL - 260
SP - 6084
EP - 6107
JO - Journal of Differential Equations
JF - Journal of Differential Equations
SN - 0022-0396
IS - 7
ER -