Evolution equations of von Karman type / Pascal Cherrier, Albert Milani

• Autore: Cherrier, Pascal
• Pubblicazione: [Cham], : Springer, : Unione matematica italiana, 2015
• Titolo uniforme: Evolution equations of von Karman type
• Descrizione fisica: XVI, 140 p. ; 24 cm
• Soggetto topico: 35F21 - Hamilton-Jacobi equations [MSC 2020]; 37J06 - General theory of finite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, invariants [MSC 2020]; 53D05 - Symplectic manifolds, general [MSC 2020]; 53D12 - Lagrangian submanifolds; Maslov index [MSC 2020]; 53Zxx - Applications of differential geometry to sciences and engineering [MSC 2020]; 58E05 - Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces [MSC 2020]
• Soggetto non controllato: Local and global solutions; Nonlinear evolution equations; Partial differential equations; Von Karman equations; Weak and strong solutions
• Persona (resp. second.): Milani, Albert
• Nota di contenuto: In these notes we consider two kinds of nonlinear evolution problems of von Karman type on Euclidean spaces of arbitrary even dimension. Each of these problems consists of a system that results from the coupling of two highly nonlinear partial differential equations, one hyperbolic or parabolic and the other elliptic. These systems take their name from a formal analogy with the von Karman equations in the theory of elasticity in two dimensional space. We establish local (respectively global) results for strong (resp., weak) solutions of these problems and corresponding well-posedness results in the Hadamard sense. Results are found by obtaining regularity estimates on solutions which are limits of a suitable Galerkin approximation scheme. The book is intended as a pedagogical introduction to a number of meaningful application of classical methods in nonlinear Partial Differential Equations of Evolution. The material is self-contained and most proofs are given in full detail. The interested reader will gain a deeper insight into the power of nontrivial a priori estimate methods in the qualitative study of nonlinear differential equations.
• Titolo autorizzato: Evolution equations of von Karman type
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: VAN00113685
• Lo trovi qui: Univ. Vanvitelli
• Localizzazioni e accesso elettronico: http://dx.doi.org/10.1007/978-3-319-20997-5
• Serie: Lecture notes of the Unione Matematica Italiana Berlin [etc.] . -Springer ; 17