Stationary solutions, intermediate asymptotics and large-time behaviour of type II Streater's models
Karch, Grzegorz; Biler, Piotr; Dolbeault, Jean; Esteban, Maria J. (2001), Stationary solutions, intermediate asymptotics and large-time behaviour of type II Streater's models, Advances in Differential Equations, 6, 4, p. 461-480
TypeArticle accepté pour publication ou publié
Journal nameAdvances in Differential Equations
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Abstract (EN)The authors consider type II Streater's models which describe the coupled evolution of the density of a cloud of particles in an external potential with non-constant temperature. Energy is preserved. The authors introduce an entropy and investigate stationary solutions in a bounded domain, or in an unbounded domain with confining external potential. Existence and uniqueness results for stationary solutions are established. The entropy is re-interpreted as a relative entropy which controls the convergence to stationary solutions. Also, the whole-space setting without exterior potential is considered. The authors employ time-dependent scalings and show existence of intermediate asymptotics in special cases.
Subjects / KeywordsStreater’s models; drift-diﬀusion systems; relative entropy; asymptotic behavior of solutions; conﬁnement; convex functional; a priori estimates; mass/charge; energy; existence and uniqueness of stationary solutions; rate of convergence; time-dependent rescalings; intermediate asymptotics
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