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The Solution Of Nonhomogen Abstract Cauchy Problem by Semigroup Theory of Linear Operator

Journal Of Natural Sciences And Mathematics Research

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Title The Solution Of Nonhomogen Abstract Cauchy Problem by Semigroup Theory of Linear Operator
 
Creator Hariyanto, Susilo
 
Subject applied mathematics
Degenerate; Nondegenerate; Cauchy Problem; Infinitesimal
 
Description In this article we will investigate how to solve nonhomogen degenerate Cauchy problem via theory of semigroup of linear operator. The problem is formulated in Hilbert space which can be written as direct sum of subset Ker M and Ran M*. By certain assumptions the problem can be reduced to nondegenerate Cauchy problem. And then by composition between invers of operator M and the nondegenerate problem we can transform it to canonic problem, which is easier to solve than the original problem. By taking assumption that the operator A is infinitesimal generator of semigroup, the canonic problem has a unique solution. This allow to define special operator which map the solution of canonic problem to original problem. ©2016 JNSMR UIN Walisongo. All rights reserved.
 
Publisher Faculty of Science and Technology, Universitas Islam Negeri Walisongo Semarang
 
Contributor Mathematics Department, Faculty of Mathematics and Natural Science, Universitas Diponegoro
 
Date 2017-08-24
 
Type info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
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Format application/pdf
 
Identifier https://journal.walisongo.ac.id/index.php/JNSMR/article/view/1656
10.21580/jnsmr.2016.1.2.1656
 
Source Journal Of Natural Sciences And Mathematics Research; Vol 2, No 2 (2016): Volume 2, Nomor 2, 2016; 143-147
2460-4453
2614-6487
 
Language eng
 
Relation https://journal.walisongo.ac.id/index.php/JNSMR/article/view/1656/1235
 
Rights Copyright (c) 2017 Journal Of Natural Sciences And Mathematics Research