Coleman-Gurtin模型的渐近性
Asymptotics of the Coleman-Gurtin model
摘要：
本文研究了Coleman-Gurtin的遗传记忆热传导理论中的积分微分方程$$\partial_t u-Δu -\int_0^\infty κ(s)Δu(t-s)\,\d s + φ(u)=f$$，其中存在临界增长的非线性$φ$。在历史空间框架内改写该方程，证明了相关解半群存在具有最佳正则性和有限分维的全局和指数吸引子，它们既作用在基本弱能量空间上，又作用在更规则的相空间上。
英文摘要：
This paper is concerned with the integrodifferential equation $$\partial_t u-Δu -\int_0^\infty κ(s)Δu(t-s)\,\d s + φ(u)=f$$ arising in the Coleman-Gurtin's theory of heat conduction with hereditary memory, in presence of a nonlinearity $φ$ of critical growth. Rephrasing the equation within the history space framework, we prove the existence of global and exponential attractors of optimal regularity and finite fractal dimension for the related solution semigroup, acting both on the basic weak-energy space and on a more regular phase space.
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