03943nam a22005295i 4500 978-0-8176-8117-3 DE-He213 20260521092033.0 cr nn 008mamaa 110615s2011 xxu| s |||| 0|eng d 9780817681173 99780817681173 10.1007/978-0-8176-8117-3 doi 515.353 23 Rabinowitz, Paul H. author. Extensions of Moser-Bangert Theory [electronic resource] : Locally Minimal Solutions / by Paul H. Rabinowitz, Edward W. Stredulinsky. Boston : Birkhäuser Boston, 2011. VIII, 208p. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Progress in Nonlinear Differential Equations and Their Applications ; 81 1 Introduction -- Part I: Basic Solutions -- 2 Function Spaces and the First Renormalized Functional -- 3 The Simplest Heteroclinics -- 4 Heteroclinics in x1 and x2 -- 5 More Basic Solutions -- Part II: Shadowing Results -- 6 The Simplest Cases -- 7 The Proof of Theorem 6.8 -- 8 k-Transition Solutions for k > 2 -- 9 Monotone 2-Transition Solutions -- 10 Monotone Multitransition Solutions -- 11 A Mixed Case -- Part III: Solutions of (PDE) Defined on R^2 x T^{n-2} -- 12 A Class of Strictly 1-Monotone Infinite Transition Solutions of (PDE) -- 13 Solutions of (PDE) with Two Transitions in x1 and Heteroclinic Behavior in x2. With the goal of establishing a version for partial differential equations (PDEs) of the Aubry-Mather theory of monotone twist maps, Moser and then Bangert studied solutions of their model equations that possessed certain minimality and monotonicity properties. This monograph presents extensions of the Moser-Bangert approach that include solutions of a family of nonlinear elliptic PDEs on Rn and an Allen-Cahn PDE model of phase transitions. After recalling the relevant Moser-Bangert results, Extensions of Moser-Bangert Theory pursues the rich structure of the set of solutions of a simpler model case, expanding upon the studies of Moser and Bangert to include solutions that merely have local minimality properties. Subsequent chapters build upon the introductory results, making the monograph self contained. Part I introduces a variational approach involving a renormalized functional to characterize the basic heteroclinic solutions obtained by Bangert. Following that, Parts II and III employ these basic solutions together with constrained minimization methods to construct multitransition heteroclinic and homoclinic solutions on R×Tn-1 and R2×Tn-2, respectively, as local minima of the renormalized functional. The work is intended for mathematicians who specialize in partial differential equations and may also be used as a text for a graduate topics course in PDEs. MATHEMATICS. FOOD SCIENCE. GLOBAL ANALYSIS (MATHEMATICS). DIFFERENTIABLE DYNAMICAL SYSTEMS. DIFFERENTIAL EQUATIONS, PARTIAL. MATHEMATICAL OPTIMIZATION. MATHEMATICS. PARTIAL DIFFERENTIAL EQUATIONS. CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION. DYNAMICAL SYSTEMS AND ERGODIC THEORY. ANALYSIS. FOOD SCIENCE. Stredulinsky, Edward W. author. SpringerLink (Online service) Springer eBooks Printed edition: 9780817681166 Progress in Nonlinear Differential Equations and Their Applications ; 81 http://dx.doi.org/10.1007/978-0-8176-8117-3 Ver el texto completo en las instalaciones del CICY ZDB-2-SMA ddc ER 35786 35786 0 0 ddc 0 0 LE CICY CICY EL 2025-10-06 0 515.353 2025-10-06 08:44:40 2025-10-06 ER