Analysis of District Heating Networks

被引：0

作者：

Borsche, R. ^{[1
]}

Eimer, M. ^{[2
]}

Garavello, M. ^{[3
]}

Rossi, E. ^{[4
]}

机构：

[1] TU Kaiserslautern, Erwin Schrodinger Str, D-67663 Kaiserslautern, Germany

[2] Fraunhofer Inst Ind Math ITWM, Fraunhofer Platz 1, D-67663 Kaiserslautern, Germany

[3] Univ Milano Bicocca, Dept Math & Applicat, Via R Cozzi 55, I-20125 Milan, Italy

[4] Univ Modena & Reggio Emilia, Dept Sci & Methods Engn, Via Amendola 2, Pad Morselli, I-42122 Reggio Emilia, Italy

来源：

APPLIED MATHEMATICS AND OPTIMIZATION | 2023年 / 87卷 / 03期

关键词：

District heating networks; Mixed ODE-PDE system; Control problems; CONSERVATION-LAWS; P-SYSTEM; BOUNDARY;

D O I：

10.1007/s00245-022-09952-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the context of district heating networks we consider a model for the distribution of energy through water (for heating or cooling) from a central power station to the consumers. We prove the well posedness of the system, by using the Banach Fixed Point Theorem together with stability estimates for reduced systems. Eventually we consider optimal control problems motivated by applications and we provide the existence of optimal controls in special situations.

引用

页数：36

共 34 条

[1] Banach S., 1922, FUND MATH, V3, P133, DOI [DOI 10.4064/FM-3-1-133-181, 10.4064/fm-3-1-133-181]
[2] A local time stepping method for thermal energy transport in district heating networks
Borsche, Raul
Eimer, Matthias
Siedow, Norbert
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2019, 353 : 215 - 229
[3] Mixed systems: ODEs - Balance laws
Borsche, Raul
Colombo, Rinaldo M.
Garavello, Mauro
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2012, 252 (03) : 2311 - 2338
[4] Boyd S., 2004, CONVEX OPTIMIZATION, DOI [DOI 10.1017/CBO9780511804441, 10.1017/CBO9780511804441]
[5] Bressan A., 2007, Introduction to the Mathematical Theory of Control
[6] CODDINGTON E. A., 1955, THEORY ORDINARY DIFF
[7] ON 2 x 2 CONSERVATION LAWS AT A JUNCTION
Colombo, R. M.
Herty, M.
Sachers, V.
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2008, 40 (02) : 605 - 622
[8] OPTIMAL CONTROL IN NETWORKS OF PIPES AND CANALS
Colombo, R. M.
Guerra, G.
Herty, M.
Schleper, V.
[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2009, 48 (03) : 2032 - 2050
[9] Colombo R.M., 2021, PREPRINT
[10] On the Cauchy problem for the p-system at a junction
Colombo, Rinaldo M.
Garavello, Mauro
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2008, 39 (05) : 1456 - 1471

← 1 2 3 4 →