Balance Laws -- to Continuum Physics -- Hyperbolic Systems of Balance Laws -- The Cauchy Problem -- Entropy and the Stability of Classical Solutions -- The L1 Theory for Scalar Conservation Laws -- Hyperbolic Systems of Balance Laws in One-Space Dimension -- Admissible Shocks -- Admissible Wave Fans and the Riemann Problem -- Generalized Characteristics. -- Genuinely Nonlinear Scalar Conservati…
Homological Methods in Fixed Point Theory -- Coincidence Theory -- On the Lefschetz Fixed Point Theorem -- Linearizations for Maps of Nilmanifolds and Solvmanifolds -- Homotopy Minimal Periods -- Periodic Points and Braid Theory -- Fixed Point Theory of Multivalued Weighted Maps -- Fixed Point Theory for Homogeneous Spaces A Brief Survey -- Equivariant Fixed Point Theory -- A Note on Equivarian…
A. Giorgilli: Preface -- G. Benettin: Physical Applications of Nekhoroshev Theorem and Exponential Estimates -- J. Henrard: The Adiabatic Invariant Theory and Applications -- S. Kuksin: Lectures on Hamiltonian Methods in Nonlinear PDEs.This volume collects three series of lectures on applications of the theory of Hamiltonian systems, contributed by some of the specialists in the field. The aim …
Introductory Chapter -- Laplace Operators on Riemannian Manifolds -- Lagrangian Formalism on Riemannian Manifolds -- Harmonic Maps from a Lagrangian Viewpoint -- Conservation Theorems -- Hamiltonian Formalism -- Hamilton-Jacobi Theory -- Minimal Hypersurfaces -- Radially Symmetric Spaces -- Fundamental Solutions for Heat Operators with Potentials -- Fundamental Solutions for Elliptic Operators …
Summary -- Background -- Fundamental Theorem -- Trudinger-Moser Inequality -- The Green’s Function -- Equilibrium States -- Blowup Analysis for Stationary Solutions -- Multiple Existence -- Dynamical Equivalence -- Formation of Collapses -- Finiteness of Blowup Points -- Concentration Lemma -- Weak Solution -- Hyperparabolicity -- Quantized Blowup Mechanism -- Theory of Dual Variation.This bo…
Diffusione -- Equazione di Laplace -- Equazioni del primo ordine -- Onde -- Analisi funzionale -- Formulazioni variazionali.La presente raccolta di problemi ed esercizi nasce dall'esperienza maturata durante il corso di Equazioni a Derivate Parziali (EDP), tenuto nell'ambito delle lauree di primo e secondo livello presso il Politecnico di Milano. Il volume è diviso in due parti; nei primi quat…
One-Layer Free Boundary Problems with Two Free Boundaries -- New Numerical Solutions for the Brezis-Nirenberg Problem on $$\mathbb{S}^n $$ -- On some Boundary Value Problems for Incompressible Viscous Flows with Shear Dependent Viscosity -- Radiative Heat Transfer in Silicon Purification -- A Decay Result for a Quasilinear Parabolic System -- The Shape of Charged Drops: Symmetrybreaking Bifurc…
Symbolic Computation of Lyapunov Quantities and the Second Part of Hilbert’s Sixteenth Problem -- Estimating Limit Cycle Bifurcations from Centers -- Conditions of Infinity to be an Isochronous Center for a Class of Differential Systems -- Darboux Integrability and Limit Cycles for a Class of Polynomial Differential Systems -- Time-Reversibility in Two-Dimensional Polynomial Systems -- On Sym…
Measures and Transforms -- Selfadjointness and Spectrum -- Criteria for Identifying the Spectrum -- Operators of Interest -- Applications.Themainobjectiveofthisbookistogiveacollectionofcriteriaavailablein the spectral theory of selfadjoint operators, and to identify the spectrum and its components in the Lebesgue decomposition. Many of these criteria were published in several articles in di?ere…
General Definitions, Conservation Laws -- Lagrangian Coordinates -- Constitutive Laws -- The Principle of Material Frame-Indifference -- Replacing Entropy with Temperature -- Isotropy -- Equations in Lagrangian Coordinates -- Linearized Models -- Quasi-static Thermoelasticity -- Fluids -- Linearized Models for Fluids, Acoustics -- Perfect Gases -- Incompressible Fluids -- Turbulent Flow of Inco…