TY - JOUR
T1 - Minimal solutions of a semilinear elliptic equation with a dynamical boundary condition
AU - Fila, Marek
AU - Ishige, Kazuhiro
AU - Kawakami, Tatsuki
N1 - Funding Information:
The first author was supported by the Slovak Research and Development Agency under the contract No. APVV-0134-10 and by the VEGA grant 1/0319/15 . The second author was supported by the Grant-in-Aid for Scientific Research (B) (No. 23340035 ) from Japan Society for the Promotion of Science . The third author was supported by the Grant-in-Aid for Young Scientists (B) (No. 24740107 ) from Japan Society for the Promotion of Science .
Publisher Copyright:
© 2015 Elsevier Masson SAS.
PY - 2016/6/1
Y1 - 2016/6/1
N2 - We study properties of positive solutions of a semilinear elliptic equation with a linear dynamical boundary condition. We establish the semigroup property for minimal solutions, show that every local-in-time solution can be extended globally, and reveal a relationship between minimal solutions of the time-dependent problem and minimal solutions of a corresponding stationary problem.
AB - We study properties of positive solutions of a semilinear elliptic equation with a linear dynamical boundary condition. We establish the semigroup property for minimal solutions, show that every local-in-time solution can be extended globally, and reveal a relationship between minimal solutions of the time-dependent problem and minimal solutions of a corresponding stationary problem.
KW - Dynamical boundary condition
KW - Minimal solutions
KW - Phragmén-Lindelöf theorem
KW - Semilinear elliptic equation
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U2 - 10.1016/j.matpur.2015.11.014
DO - 10.1016/j.matpur.2015.11.014
M3 - Article
AN - SCOPUS:84958280943
SN - 0021-7824
VL - 105
SP - 788
EP - 809
JO - Journal des Mathematiques Pures et Appliquees
JF - Journal des Mathematiques Pures et Appliquees
IS - 6
ER -