DETERMINATION OF THE FRACTIONAL ORDER IN SEMILINEAR SUBDIFFUSION EQUATIONS

被引：9

作者：

Krasnoschok, Mykola ^{[1
]}

Pereverzyev, Sergei ^{[2
]}

Siryk, Sergii, V ^{[3
]}

Vasylyeva, Nataliya ^{[1
]}

机构：

[1] NAS Ukraine, Inst Appl Math & Mech, G Batyuka Str 19, UA-84100 Sloviansk, Ukraine

[2] Johann Radon Inst, A-040 Linz, Austria

[3] Natl Tech Univ Ukraine, Igor Sikorsky Kyiv Polytech Inst, Prospect Peremohy 37, UA-03056 Kiev, Ukraine

来源：

FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2020年 / 23卷 / 03期

基金：

欧盟地平线“2020”;

关键词：

materials with memory; subdiffusion semilinear equations; Caputo derivative; inverse problem; regularization method; quasioptimality approach; INVERSE PROBLEMS; DIFFUSION; CALCULUS; TERM;

D O I：

10.1515/fca-2020-0035

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We analyze the inverse boundary value-problem to determine the fractional order. of nonautonomous semilinear subdiffusion equations with memory terms from observations of their solutions during small time. We obtain an explicit formula reconstructing the order. Based on the Tikhonov regularization scheme and the quasi-optimality criterion, we construct the computational algorithm to find the order. from noisy discrete measurements. We present several numerical tests illustrating the algorithm in action.

引用

页码：694 / 722

页数：29

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