000			03750cam a2200373 a 4500
999			_c3937 _d3937
001			15924604
003			NG-AbAUS
005			20230307093518.0
008			090928s2010 riua b 001 0 eng
010			_a 2009037756
020			_a9780821849040 (alk. paper)
020			_a0821849042 (alk. paper)
035			_a(OCoLC)ocn441945348
040			_aDLC _cDLC _dYDX _dYDXCP _dUBY _dIXA _dDLC
041	1		_aeng _hger
050	0	0	_aQA402.3 _b.T71913 2010
082	0	0	_222
100	1		_aTröltzsch, Fredi, _d1951- _9320
240	1	0	_aOptimale Steuerung partieller Differentialgleichungen. _lEnglish
245	1	0	_aOptimal control of partial differential equations : _btheory, methods, and applications / _cFredi Tröltzsch ; translated by Jürgen Sprekels.
260			_aProvidence, R.I. : _bAmerican Mathematical Society, _cc2010.
300			_axv, 399 p. : _bill. ; _c26 cm.
490	1		_aGraduate studies in mathematics : _vv. 112
504			_aIncludes bibliographical references and index.
505	0		_aIntroduction and examples -- Linear-quadratic elliptic control problems -- Linear-quadratic parabolic control problems -- Optimal control of semilinear elliptic equations -- Optimal control of semilinear parabolic equations -- Optimization problems in Banach spaces -- Supplementary results on partial differential equations.
520			_a"Optimal control theory is concerned with finding control functions that minimize cost functions for systems described by differential equations. The methods have found widespread applications in aeronautics, mechanical engineering, the life sciences, and many other disciplines. This book focuses on optimal control problems where the state equation is an elliptic or parabolic partial differential equation. Included are topics such as the existence of optimal solutions, necessary optimality conditions and adjoint equations, second-order sufficient conditions, and main principles of selected numerical techniques. It also contains a survey on the Karush-Kuhn-Tucker theory of nonlinear programming in Banach spaces. The exposition begins with control problems with linear equations, quadratic cost functions and control constraints. To make the book self-contained, basic facts on weak solutions of elliptic and parabolic equations are introduced. Principles of functional analysis are introduced and explained as they are needed. Many simple examples illustrate the theory and its hidden difficulties. This start to the book makes it fairly self-contained and suitable for advanced undergraduates or beginning graduate students. Advanced control problems for nonlinear partial differential equations are also discussed. As prerequisites, results on boundedness and continuity of solutions to semilinear elliptic and parabolic equations are addressed. These topics are not yet readily available in books on PDEs, making the exposition also interesting for researchers. Alongside the main theme of the analysis of problems of optimal control, Tröltzsch also discusses numerical techniques. The exposition is confined to brief introductions into the basic ideas in order to give the reader an impression of how the theory can be realized numerically. After reading this book, the reader will be familiar with the main principles of the numerical analysis of PDE-constrained optimization."--Publisher's description.
650		0	_aControl theory. _9321
650		0	_aDifferential equations, Partial. _9294
650		0	_aMathematical optimization. _9322
830		0	_aGraduate studies in mathematics ; _vv. 112. _9323
906			_a7 _bcbc _corignew _d1 _eecip _f20 _gy-gencatlg
942			_2lcc _cBK
955			_bxh00 2009-09-28 _ixh07 2009-09-28 to Dewey _axe06 2010-07-14 1 copy rec'd., to CIP ver.