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- W1594549216 abstract "Abstract: We consider a distributed system with persistent memory of atype which is often encountered in viscoelasticity or in the study of diffusionprocesses with memory. The relaxation kernel, i.e. the kernel of the memoryterm, is scarcely known from first principles, and it has to be inferred fromexperiments taken on samples of the material. We prove that two boundarymeasures give a linear Volterra integral equation of the first kind for theunknown kernel. Hence, with two measures, the identification of the kernel,which in principle is a nonlinear problem, is reduced to the solution of amildly ill posed but linear problem. 1 Introduction Let w = w(x,t), t > 0 and x ∈ Ω (a bounded region with smooth boundary).The equation with persistent memory (∆ is the laplacian)w ′ =Z t0 N(t −s)∆w(s) ds (1.1)is encountered in thermodynamics of systems with memory (w is the temper-ature) in nonfickian diffusion (w is the concentration) or in viscoelasticity. In ∗ This papers fits into the research program of the GNAMPA-INDAM and has beenwritten in the framework of the “Groupement de Recherche en Contrˆole des EDP entre laFrance et l’Italie (CONEDP-CNRS)”." @default.
- W1594549216 created "2016-06-24" @default.
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- W1594549216 date "2015-03-12" @default.
- W1594549216 modified "2023-09-27" @default.
- W1594549216 title "Identification of a relaxation kernel using two boundary measures" @default.
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