Gilles Lebeau - Böcker
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6 produkter
6 produkter
643 kr
Skickas inom 7-10 vardagar
This book presents the analytic foundations to the theory of the hypoelliptic Laplacian. The hypoelliptic Laplacian, a second-order operator acting on the cotangent bundle of a compact manifold, is supposed to interpolate between the classical Laplacian and the geodesic flow. Jean-Michel Bismut and Gilles Lebeau establish the basic functional analytic properties of this operator, which is also studied from the perspective of local index theory and analytic torsion. The book shows that the hypoelliptic Laplacian provides a geometric version of the Fokker-Planck equations. The authors give the proper functional analytic setting in order to study this operator and develop a pseudodifferential calculus, which provides estimates on the hypoelliptic Laplacian's resolvent. When the deformation parameter tends to zero, the hypoelliptic Laplacian converges to the standard Hodge Laplacian of the base by a collapsing argument in which the fibers of the cotangent bundle collapse to a point. For the local index theory, small time asymptotics for the supertrace of the associated heat kernel are obtained.The Ray-Singer analytic torsion of the hypoelliptic Laplacian as well as the associated Ray-Singer metrics on the determinant of the cohomology are studied in an equivariant setting, resulting in a key comparison formula between the elliptic and hypoelliptic analytic torsions.
Del 98 - Progress in Nonlinear Differential Equations and Their Applications
Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume II
General Boundary Conditions on Riemannian Manifolds
Inbunden, Engelska, 2022
1 107 kr
Skickas inom 5-8 vardagar
This monograph explores applications of Carleman estimates in the study of stabilization and controllability properties of partial differential equations, including quantified unique continuation, logarithmic stabilization of the wave equation, and null-controllability of the heat equation.
Del 98 - Progress in Nonlinear Differential Equations and Their Applications
Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume II
General Boundary Conditions on Riemannian Manifolds
Häftad, Engelska, 2023
1 107 kr
Skickas inom 5-8 vardagar
This monograph explores applications of Carleman estimates in the study of stabilization and controllability properties of partial differential equations, including quantified unique continuation, logarithmic stabilization of the wave equation, and null-controllability of the heat equation.
Del 97 - Progress in Nonlinear Differential Equations and Their Applications
Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume I
Dirichlet Boundary Conditions on Euclidean Space
Inbunden, Engelska, 2022
898 kr
Skickas inom 5-8 vardagar
This monograph explores applications of Carleman estimates in the study of stabilization and controllability properties of partial differential equations, including the stabilization property of the damped wave equation and the null-controllability of the heat equation.
Del 97 - Progress in Nonlinear Differential Equations and Their Applications
Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume I
Dirichlet Boundary Conditions on Euclidean Space
Häftad, Engelska, 2023
898 kr
Skickas inom 5-8 vardagar
This monograph explores applications of Carleman estimates in the study of stabilization and controllability properties of partial differential equations, including the stabilization property of the damped wave equation and the null-controllability of the heat equation.
Del 1723 - Lecture Notes in Mathematics
Diffraction by an Immersed Elastic Wedge
Häftad, Engelska, 1999
324 kr
Skickas inom 10-15 vardagar
This monograph presents the mathematical description and numerical computation of the high-frequency diffracted wave by an immersed elastic wave with normal incidence. The mathematical analysis is based on the explicit description of the principal symbol of the pseudo-differential operator connected with the coupled linear problem elasticity/fluid by the wedge interface. This description is subsequently used to derive an accurate numerical computation of diffraction diagrams for different incoming waves in the fluid, and for different wedge angles. The method can be applied to any problem of coupled waves by a wedge interface. This work is of interest for any researcher concerned with high frequency wave scattering, especially mathematicians, acousticians, engineers.