The author studies semilinear parabolic equations with initial and periodic boundary value conditions. In the presence of non-well-ordered sub- and super-solutions： ＂subsolution ≮ supersolution＇, the existence and...The author studies semilinear parabolic equations with initial and periodic boundary value conditions. In the presence of non-well-ordered sub- and super-solutions： ＂subsolution ≮ supersolution＇, the existence and stability/instability of equilibrium solutions are obtained.展开更多
The purpose of this paper is to study the asymptotic behavior of the positive solutions of the problemt ■tu-△u=au-b(x)up inΩ×R+,u(0)=u0,u(t)|■Ω=0,as p → +∞,where Ω is a bounded domain,and b(x) is a nonneg...The purpose of this paper is to study the asymptotic behavior of the positive solutions of the problemt ■tu-△u=au-b(x)up inΩ×R+,u(0)=u0,u(t)|■Ω=0,as p → +∞,where Ω is a bounded domain,and b(x) is a nonnegative function.The authors deduce that the limiting configuration solves a parabolic obstacle problem,and afterwards fully describe its long time behavior.展开更多
基金Partially supported by the project-sponsored by SRF for ROCS, SEM
文摘The author studies semilinear parabolic equations with initial and periodic boundary value conditions. In the presence of non-well-ordered sub- and super-solutions： ＂subsolution ≮ supersolution＇, the existence and stability/instability of equilibrium solutions are obtained.
基金Project supported by Fundaco para a Ciência e a Tecnologia (FCT) (No. PEst OE/MAT/UI0209/2011)supported by an FCT grant (No. SFRH/BPD/69314/201)
文摘The purpose of this paper is to study the asymptotic behavior of the positive solutions of the problemt ■tu-△u=au-b(x)up inΩ×R+,u(0)=u0,u(t)|■Ω=0,as p → +∞,where Ω is a bounded domain,and b(x) is a nonnegative function.The authors deduce that the limiting configuration solves a parabolic obstacle problem,and afterwards fully describe its long time behavior.
