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…
Fondamenti degli elementi finiti -- Problemi stazionari -- Il metodo di Galerkin-elementi finiti per problemi di tipo ellittico -- Problemi di diffusione, trasporto e reazione -- Il metodo delle differenze finite -- Problemi tempo-dipendenti -- Equazioni di tipo parabolico -- Equazioni di tipo iperbolico -- Equazioni di Navier-Stokes per fluidi a densità costante.Questo testo contiene una racc…
to Boundary-Value Problems -- Compact Self-Adjoint Operators -- Topics in Euclidean Fourier Analysis -- Topics in Functional Analysis -- Distributions -- Compact and Locally Compact Groups -- Aspects of Partial Differential Equations -- Analysis on Manifolds -- Foundations of Probability.Basic Real Analysis and Advanced Real Analysis (available separately or together as a Set) systematically de…
Differential Mathematical Models -- Integrable Differential Equations -- Dynamic Model of Systems with Heat Generation -- Stiff Differential Equations -- Heat Transfer near the Stagnation Point at Cross Tube Flow -- The Falkner-Skan Equation of Boundary Layer -- Rayleigh’s Equation: Hydrodynamical Instability -- Kinematic Waves of Concentration in Ion-Exchange Filter -- Kinematic Shock Waves …
This volume is an expanded version of Chapters III, IV, V and VII of my 1963 book "Linear partial differential operators". In addition there is an entirely new chapter on convolution equations, one on scattering theory, and one on methods from the theory of analytic functions of several complex variables. The latter is somewhat limited in scope though since it seems superfluous to duplicate the…