کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
840176 | 1470515 | 2013 | 15 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Positive stationary solutions and threshold results for the non-homogeneous semilinear parabolic equation with Robin boundary conditions Positive stationary solutions and threshold results for the non-homogeneous semilinear parabolic equation with Robin boundary conditions](/preview/png/840176.png)
Let ΩΩ be a smooth bounded domain in RnRn. Considering the following Robin problem for a semilinear parabolic equation equation(0.1){ut−Δu=up+f(x),(x,t)∈Ω×(0,T),∂u∂ν+βu=0,(x,t)∈∂Ω×[0,T),u(x,0)=u0(x),x∈Ω, we show that for any function f(x)f(x) satisfying (F)(F) which will be given in the introduction, there exists a positive number βf⋆ such that problem (0.1) has no stationary solution if β∈(0,βf⋆), and has at least two stationary solutions when β>βf⋆. Moreover, among all stationary solutions of problem (0.1) there is a minimal one. We prove further that the minimal stationary solution of problem (0.1) is stable, whereas, any other stationary solutions of problem (0.1) are initial datum thresholds for the existence and non-existence of a global solution to problem (0.1).
Journal: Nonlinear Analysis: Theory, Methods & Applications - Volume 85, July 2013, Pages 233–247