Lecture notes in applied differential equations of mathematical physics / Luiz C.L. Botelho.

Format:

Book

Author/Creator:

Botelho, Luiz C. L.

Language:

English

Subjects (All):

Differential equations.

Functional analysis.

Mathematical physics.

Physical Description:

1 online resource (340 p.)

Edition:

1st ed.

Place of Publication:

Hackensack, NJ : World Scientific, c2008.

Language Note:

English

Summary:

Functional analysis is a well-established powerful method in mathematical physics, especially those mathematical methods used in modern non-perturbative quantum field theory and statistical turbulence. This book presents a unique, modern treatment of solutions to fractional random differential equations in mathematical physics. It follows an analytic approach in applied functional analysis for functional integration in quantum physics and stochastic Langevin-turbulent partial differential equations.An errata II to the book is available. Click here to download the pdf.

Contents:

Foreword; Contents; Chapter 1. Elementary Aspects of Potential Theory in Mathematical Physics; 1.1. Introduction; 1.2. The Laplace Differential Operator and the Poisson-Dirichlet Potential Problem; 1.3. The Dirichlet Problem in Connected Planar Regions: A Conformal Transformation Method for Green Functions in String Theory; 1.4. Hilbert Spaces Methods in the Poisson Problem; 1.5. The Abstract Formulation of the Poisson Problem; 1.6. Potential Theory for the Wave Equation in R3 - Kirchho. Potentials (Spherical Means); 1.7. The Dirichlet Problem for the Diffusion Equation - Seminar Exercises

1.8. The Potential Theory in Distributional Spaces - The Gelfand-ChilovMethodReferences; Appendix A. Light Deflection on de-Sitter Space; A.1.The Light Deflection; A.2.The Trajectory Motion Equations; A.3. On the Topology of the Euclidean Space-Time; Chapter 2. Scattering Theory in Non-Relativistic One-Body Short-Range Quantum Mechanics: M ̈oller Wave Operators and Asymptotic Completeness; 2.1. The Wave Operators in One-Body Quantum Mechanics; 2.2. Asymptotic Properties of States in the Continuous Spectra of the Enss Hamiltonian

2.3. The Enss Proof of the Non-Relativistic One-Body QuantumMechanical ScatteringReferences; Appendix A; Appendix B; Appendix C; Chapter 3. On the Hilbert Space Integration Method for the Wave Equation and Some Applications to Wave Physics; 3.1. Introduction; 3.2. The Abstract Spectral Method - The Nondissipative Case; 3.3. The Abstract Spectral Method - The Dissipative Case; 3.4. The Wave Equation "Path-Integral" Propagator; 3.5. On The Existence of Wave-Scattering Operators; 3.6. Exponential Stability in Two-Dimensional Magneto-Elasticity: A Proof on a Dissipative Medium

3.7. An Abstract Semilinear Klein Gordon Wave Equation - Existence and UniquenessReferences; Appendix A. Exponential Stability in Two-Dimensional Magneto-Elastic: Another Proof; Appendix B. Probability Theory in Terms of Functional Integrals and theMinlos Theorem; Chapter 4. Nonlinear Di.usion and Wave-Damped Propagation: Weak Solutions and Statistical Turbulence Behavior.; 4.1. Introduction; 4.2. The Theorem for Parabolic Nonlinear Diffusion; 4.3. The Hyperbolic Nonlinear Damping; 4.4. A Path-Integral Solution for the Parabolic Nonlinear Diffusion

4.5. Random Anomalous Diffuusion, A Semigroup ApproachReferences; Appendix A; Appendix B; Appendix C; Appendix D. Probability Theory in Terms of Functional Integrals and the Minlos Theorem - An Overview; Chapter 5. Domains of Bosonic Functional Integrals and Some Applications to the Mathematical Physics of Path-Integrals and String Theory; 5.1. Introduction; 5.2. The Euclidean Schwinger Generating Functional as a Functional Fourier Transform; 5.3. The Support of Functional Measures - The Minlos Theorem; 5.4. Some Rigorous Quantum Field Path-Integral in the Analytical Regularization Scheme

5.5. Remarks on the Theory of Integration of Functionals on Distributional Spaces and Hilbert-Banach Spaces

Notes:

Includes bibliographical references and index.

Includes index.

ISBN:

9789812814586

9812814582

OCLC:

820944533