TY - BOOK ID - 8580648 TI - Extensions of Moser-Bangert theory : locally minimal solutions AU - Rabinowitz, Paul H. AU - Stredulinsky, Edward W. AU - Moser, Jurgen AU - Bangert, Victor. PY - 2011 SN - 0817681167 0817681175 PB - New York : Springer, DB - UniCat KW - Differential equations, Nonlinear. KW - Differential equations, Partial. KW - Differential equations. KW - Mathematics. KW - Differential equations, Partial KW - Differential equations, Nonlinear KW - Nonlinear theories KW - Mathematics KW - Physical Sciences & Mathematics KW - Calculus KW - Mathematical analysis. KW - 517.1 Mathematical analysis KW - Mathematical analysis KW - Partial differential equations KW - Food KW - Analysis (Mathematics). KW - Dynamics. KW - Ergodic theory. KW - Partial differential equations. KW - Calculus of variations. KW - Partial Differential Equations. KW - Calculus of Variations and Optimal Control; Optimization. KW - Dynamical Systems and Ergodic Theory. KW - Analysis. KW - Food Science. KW - Biotechnology. KW - Differential equations, partial. KW - Mathematical optimization. KW - Differentiable dynamical systems. KW - Global analysis (Mathematics). KW - Food science. KW - Science KW - Analysis, Global (Mathematics) KW - Differential topology KW - Functions of complex variables KW - Geometry, Algebraic KW - Differential dynamical systems KW - Dynamical systems, Differentiable KW - Dynamics, Differentiable KW - Differential equations KW - Global analysis (Mathematics) KW - Topological dynamics KW - Optimization (Mathematics) KW - Optimization techniques KW - Optimization theory KW - Systems optimization KW - Maxima and minima KW - Operations research KW - Simulation methods KW - System analysis KW - Food—Biotechnology. KW - Dynamical systems KW - Kinetics KW - Mechanics, Analytic KW - Force and energy KW - Mechanics KW - Physics KW - Statics KW - Isoperimetrical problems KW - Variations, Calculus of KW - Ergodic transformations KW - Continuous groups KW - Mathematical physics KW - Measure theory KW - Transformations (Mathematics) UR - https://www.unicat.be/uniCat?func=search&query=sysid:8580648 AB - 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. ER -