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On the Truncation of the Infinite Sum of Exponentials in a Memory Kernel of the Linear Wave Equation
Author(s) -
Kroller M.,
Propst G.
Publication year - 1999
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/(sici)1521-4001(199909)79:9<603::aid-zamm603>3.0.co;2-j
Subject(s) - exponential function , truncation (statistics) , mathematics , semigroup , kernel (algebra) , cauchy distribution , mathematical analysis , pure mathematics , statistics
We consider the one‐dimensional wave equation with a damping term that convolves the past history with an infinite sum of exponentials. The system is reformulated as an abstract Cauchy problem. By means of semigroup theory it is shown that the systems with truncated sum of exponentials approximate the original one in L 2 sense. On the other hand it is demonstrated that the system and the approximations have different spectral properties.