کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4604899 | 1337480 | 2007 | 19 صفحه PDF | دانلود رایگان |
We establish the existence theorem and study the long time behaviour of the following PDE problem:equation(0.1){ut−div∇W(∇u)−f(x)=0in Ω×(0,−∞),∇W(∇u)⋅n|∂Ω×(0,∞)=0,u(x,0)=u0(x)in Ω where W is a specially given quasiconvex double-well function and f∈L2(Ω)f∈L2(Ω) is a given function independent of time t. In particular, the existence theorem is established for general given source term f , the long time behaviour is analyzed under the assumption that ∫Ωf(x)dx=0.The system is an evolutionary quasimonotone system. We believe that the existence of solutions established here is stronger than the usual Young Measure solution and is the first of its kind. The existence of a compact ω -limit set as t→∞t→∞ is also established under some non-restrictive conditions.
Journal: Annales de l'Institut Henri Poincare (C) Non Linear Analysis - Volume 24, Issue 3, May–June 2007, Pages 341–359