Beyond Partial Differential Equations
Beyer, Horst Reinhard.
Beyond Partial Differential Equations On Linear and Quasi-Linear Abstract Hyperbolic Evolution Equations / [electronic resource] : by Horst Reinhard Beyer. - XIV, 283 p. online resource. - Lecture Notes in Mathematics, 1898 0075-8434 ; . - Lecture Notes in Mathematics, 1898 .
Conventions -- Mathematical Introduction -- Prerequisites -- Strongly Continuous Semigroups -- Examples of Generators of Strongly Continuous Semigroups -- Intertwining Relations, Operator Homomorphisms -- Examples of Constrained Systems -- Kernels, Chains, and Evolution Operators -- The Linear Evolution Equation -- Examples of Linear Evolution Equations -- The Quasi-Linear Evolution Equation -- Examples of Quasi-Linear Evolution Equations.
The present volume is self-contained and introduces to the treatment of linear and nonlinear (quasi-linear) abstract evolution equations by methods from the theory of strongly continuous semigroups. The theoretical part is accessible to graduate students with basic knowledge in functional analysis. Only some examples require more specialized knowledge from the spectral theory of linear, self-adjoint operators in Hilbert spaces. Particular stress is on equations of the hyperbolic type since considerably less often treated in the literature. Also, evolution equations from fundamental physics need to be compatible with the theory of special relativity and therefore are of hyperbolic type. Throughout, detailed applications are given to hyperbolic partial differential equations occurring in problems of current theoretical physics, in particular to Hermitian hyperbolic systems. This volume is thus also of interest to readers from theoretical physics.
9783540711292
10.1007/978-3-540-71129-2 doi
Global analysis (Mathematics).
Operator theory.
Differential equations, partial.
Analysis.
Operator Theory.
Partial Differential Equations.
QA299.6-433
515
Beyond Partial Differential Equations On Linear and Quasi-Linear Abstract Hyperbolic Evolution Equations / [electronic resource] : by Horst Reinhard Beyer. - XIV, 283 p. online resource. - Lecture Notes in Mathematics, 1898 0075-8434 ; . - Lecture Notes in Mathematics, 1898 .
Conventions -- Mathematical Introduction -- Prerequisites -- Strongly Continuous Semigroups -- Examples of Generators of Strongly Continuous Semigroups -- Intertwining Relations, Operator Homomorphisms -- Examples of Constrained Systems -- Kernels, Chains, and Evolution Operators -- The Linear Evolution Equation -- Examples of Linear Evolution Equations -- The Quasi-Linear Evolution Equation -- Examples of Quasi-Linear Evolution Equations.
The present volume is self-contained and introduces to the treatment of linear and nonlinear (quasi-linear) abstract evolution equations by methods from the theory of strongly continuous semigroups. The theoretical part is accessible to graduate students with basic knowledge in functional analysis. Only some examples require more specialized knowledge from the spectral theory of linear, self-adjoint operators in Hilbert spaces. Particular stress is on equations of the hyperbolic type since considerably less often treated in the literature. Also, evolution equations from fundamental physics need to be compatible with the theory of special relativity and therefore are of hyperbolic type. Throughout, detailed applications are given to hyperbolic partial differential equations occurring in problems of current theoretical physics, in particular to Hermitian hyperbolic systems. This volume is thus also of interest to readers from theoretical physics.
9783540711292
10.1007/978-3-540-71129-2 doi
Global analysis (Mathematics).
Operator theory.
Differential equations, partial.
Analysis.
Operator Theory.
Partial Differential Equations.
QA299.6-433
515