EXACT SOLUTION OF THE CAUCHY PROBLEM FOR 2-D SCALAR CONSERVATION LAWS WITH CONSTANT COEFFICIENTS IN A CLASS OF DISCONTINUOUS FUNCTIONS

Mahir Resulov; Mahir Resulov; Kenan Şentürk; Kenan Senturk

Research Article

EXACT SOLUTION OF THE CAUCHY PROBLEM FOR 2-D SCALAR CONSERVATION LAWS WITH CONSTANT COEFFICIENTS IN A CLASS OF DISCONTINUOUS FUNCTIONS

Year 2012, Volume: 5 Issue: 1-2, 27 - 47, 06.05.2015

Mahir Resulov , Mahir Resulov , Kenan Şentürk , Kenan Senturk

Abstract

In this study a new method for finding exact solution of the Cauchy problem
subject to a discontinuous initial profile for the two dimensional scalar
conservation laws is suggested. For this aim, first, some properties of the
weak solution of the linearized equation are investigated. Taking these
properties into consideration an auxiliary problem having some advantages
over the main problem is introduced. The proposed auxiliary problems also
permit us to develop effective different numerical algorithms for finding the
solutions. Some computer experiments are carried out.

Keywords

Scalar conservation laws, auxiliary problem, exact and numerical solution in a class of discontinuous functions

EXACT SOLUTION OF THE CAUCHY PROBLEM FOR 2-D SCALAR CONSERVATION LAWS WITH CONSTANT COEFFICIENTS IN A CLASS OF DISCONTINUOUS FUNCTIONS

Year 2012, Volume: 5 Issue: 1-2, 27 - 47, 06.05.2015

Mahir Resulov , Mahir Resulov , Kenan Şentürk , Kenan Senturk

Abstract

Bu çalışmada iki boyutlu skaler korunum kuralları için yazılmış süreksiz
başlangıç koşullu Cauchy probleminin gerçek çözümünün bulunması için
yeni bir yöntem önerilmiştir. Bu amaçla önce, lineerleştirilmiş denklemin
zayıf çözümünün bazı özellikleri incelenmiş ve bu özellikler dikkate alınarak
esas problemde bulunmayan ve bazı avantajlara sahip yardımcı problem dahil
edilmiştir. Önerilen yardımcı problem göz önüne alınan problemin sayısal
çözümünü bulmak için etkin sayısal algoritmalar yazmaya da geniş imkan
sağlamaktadır.

Keywords

Skaler korunum yasaları, yardımcı problem, süreksiz fonksiyonlar sınıfında gerçek ve sayısal çözümler

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Details

Primary Language	English
Subjects	Engineering
Journal Section	Articles
Authors	Mahir Resulov Mahir Resulov Kenan Şentürk Kenan Senturk This is me
Publication Date	May 6, 2015
Published in Issue	Year 2012 Volume: 5 Issue: 1-2

Cite

APA	Resulov, M., Resulov, M., Şentürk, K., Senturk, K. (2015). EXACT SOLUTION OF THE CAUCHY PROBLEM FOR 2-D SCALAR CONSERVATION LAWS WITH CONSTANT COEFFICIENTS IN A CLASS OF DISCONTINUOUS FUNCTIONS. Beykent Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, 5(1-2), 27-47.
AMA	Resulov M, Resulov M, Şentürk K, Senturk K. EXACT SOLUTION OF THE CAUCHY PROBLEM FOR 2-D SCALAR CONSERVATION LAWS WITH CONSTANT COEFFICIENTS IN A CLASS OF DISCONTINUOUS FUNCTIONS. BUJSE. May 2015;5(1-2):27-47.
Chicago	Resulov, Mahir, Mahir Resulov, Kenan Şentürk, and Kenan Senturk. “EXACT SOLUTION OF THE CAUCHY PROBLEM FOR 2-D SCALAR CONSERVATION LAWS WITH CONSTANT COEFFICIENTS IN A CLASS OF DISCONTINUOUS FUNCTIONS”. Beykent Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 5, no. 1-2 (May 2015): 27-47.
EndNote	Resulov M, Resulov M, Şentürk K, Senturk K (May 1, 2015) EXACT SOLUTION OF THE CAUCHY PROBLEM FOR 2-D SCALAR CONSERVATION LAWS WITH CONSTANT COEFFICIENTS IN A CLASS OF DISCONTINUOUS FUNCTIONS. Beykent Üniversitesi Fen ve Mühendislik Bilimleri Dergisi 5 1-2 27–47.
IEEE	M. Resulov, M. Resulov, K. Şentürk, and K. Senturk, “EXACT SOLUTION OF THE CAUCHY PROBLEM FOR 2-D SCALAR CONSERVATION LAWS WITH CONSTANT COEFFICIENTS IN A CLASS OF DISCONTINUOUS FUNCTIONS”, BUJSE, vol. 5, no. 1-2, pp. 27–47, 2015.
ISNAD	Resulov, Mahir et al. “EXACT SOLUTION OF THE CAUCHY PROBLEM FOR 2-D SCALAR CONSERVATION LAWS WITH CONSTANT COEFFICIENTS IN A CLASS OF DISCONTINUOUS FUNCTIONS”. Beykent Üniversitesi Fen ve Mühendislik Bilimleri Dergisi 5/1-2 (May 2015), 27-47.
JAMA	Resulov M, Resulov M, Şentürk K, Senturk K. EXACT SOLUTION OF THE CAUCHY PROBLEM FOR 2-D SCALAR CONSERVATION LAWS WITH CONSTANT COEFFICIENTS IN A CLASS OF DISCONTINUOUS FUNCTIONS. BUJSE. 2015;5:27–47.
MLA	Resulov, Mahir et al. “EXACT SOLUTION OF THE CAUCHY PROBLEM FOR 2-D SCALAR CONSERVATION LAWS WITH CONSTANT COEFFICIENTS IN A CLASS OF DISCONTINUOUS FUNCTIONS”. Beykent Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, vol. 5, no. 1-2, 2015, pp. 27-47.
Vancouver	Resulov M, Resulov M, Şentürk K, Senturk K. EXACT SOLUTION OF THE CAUCHY PROBLEM FOR 2-D SCALAR CONSERVATION LAWS WITH CONSTANT COEFFICIENTS IN A CLASS OF DISCONTINUOUS FUNCTIONS. BUJSE. 2015;5(1-2):27-4.