Linear and semilinear partial differential equations :: an introduction /
This textbook provides a brief and lucid introduction to the theory of linear partial differential equations. It clearly explains the transition from classical to generalized solutions and the natural way in which Sobolev spaces appear as completions of spaces of continuously differentiable function...
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin ; Boston :
De Gruyter,
[2013]
|
| Series: | De Gruyter textbook.
|
| Subjects: | |
| Online Access: | DE-862 DE-863 |
| Summary: | This textbook provides a brief and lucid introduction to the theory of linear partial differential equations. It clearly explains the transition from classical to generalized solutions and the natural way in which Sobolev spaces appear as completions of spaces of continuously differentiable functions. The solution operators associated to non-homogeneous equations are used to make transition to the theory of nonlinear PDEs. Organized on three parts, this material is suitable for three one-semester courses, a beginning one in the frame of classical analysis, a more advanced course in modern theo. |
| Physical Description: | 1 online resource (xiv, 280 pages) : illustrations |
| Bibliography: | Includes bibliographical references and index. |
| ISBN: | 3110269058 9783110269055 9781299719774 1299719775 |
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| 520 | |a This textbook provides a brief and lucid introduction to the theory of linear partial differential equations. It clearly explains the transition from classical to generalized solutions and the natural way in which Sobolev spaces appear as completions of spaces of continuously differentiable functions. The solution operators associated to non-homogeneous equations are used to make transition to the theory of nonlinear PDEs. Organized on three parts, this material is suitable for three one-semester courses, a beginning one in the frame of classical analysis, a more advanced course in modern theo. | ||
| 505 | 0 | |a Preface; Notation; I Classical Theory; 1 Preliminaries; 1.1 Basic Differential Operators; 1.2 Linear and Quasilinear Partial Differential Equations; 1.3 Solutions of Some Particular Equations; 1.4 Boundary Value Problems; 1.4.1 Boundary Value Problems for Poisson's Equation; 1.4.2 Boundary Value Problems for the Heat Equation; 1.4.3 Boundary Value Problems for the Wave Equation; 2 Partial Differential Equations and Mathematical Modeling; 2.1 Conservation Laws: Continuity Equations; 2.2 Reaction-Diffusion Systems; 2.3 The One-Dimensional Wave Equation | |
| 505 | 8 | |a 2.4 Other Equations in Mathematical Physics3 Elliptic Boundary Value Problems; 3.1 Green's Formulas; 3.2 The Fundamental Solution of Laplace's Equation; 3.3 Mean Value Theorems for Harmonic Functions; 3.4 The Maximum Principle; 3.5 Uniqueness and Continuous Dependence on Data for the Dirichlet Problem; 3.6 Green's Function of the Dirichlet Problem; 3.7 Poisson's Formula; 3.8 Dirichlet's Principle; 3.9 The Generalized Solution of the Dirichlet Problem; 3.10 Abstract Fourier Series; 3.11 The Eigenvalues and Eigenfunctions of the Dirichlet Problem | |
| 505 | 8 | |a 3.12 The Case of Elliptic Equations in Divergence Form3.13 The Generalized Solution of the Neumann Problem; 3.14 Complements; 3.14.1 Harnack's Inequality; 3.14.2 Hopf's Maximum Principle; 3.14.3 The Newtonian Potential; 3.14.4 Perron's Method; 3.14.5 Layer Potentials; 3.14.6 Fredholm's Method of Integral Equations; 3.15 Problems; 4 Mixed Problems for Evolution Equations; 4.1 The Maximum Principle for the Heat Equation; 4.2 Vector-Valued Functions; 4.3 The Cauchy-Dirichlet Problem for the Heat Equation; 4.4 The Cauchy-Dirichlet Problem for the Wave Equation; 4.5 Problems | |
| 505 | 8 | |a 5 The Cauchy Problem for Evolution Equations5.1 The Fourier Transform; 5.1.1 The Fourier Transform on L1 (Rn); 5.1.2 Fourier Transform and Convolution; 5.1.3 The Fourier Transform on the Schwartz Space S (R"); 5.2 The Cauchy Problem for the Heat Equation; 5.3 The Cauchy Problem for the Wave Equation; 5.4 Nonhomogeneous Equations: Duhamel's Principle; 5.5 Problems; II Modern Theory; 6 Distributions; 6.1 The Fundamental Spaces of the Theory of Distributions; 6.2 Distributions: Examples; Operations with Distributions; 6.2.1 Regular Distributions; 6.2.2 The Dirac Distribution | |
| 650 | 0 | |a Differential equations, Linear |v Textbooks. | |
| 650 | 0 | |a Differential equations, Partial |v Textbooks. | |
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| contents | Preface; Notation; I Classical Theory; 1 Preliminaries; 1.1 Basic Differential Operators; 1.2 Linear and Quasilinear Partial Differential Equations; 1.3 Solutions of Some Particular Equations; 1.4 Boundary Value Problems; 1.4.1 Boundary Value Problems for Poisson's Equation; 1.4.2 Boundary Value Problems for the Heat Equation; 1.4.3 Boundary Value Problems for the Wave Equation; 2 Partial Differential Equations and Mathematical Modeling; 2.1 Conservation Laws: Continuity Equations; 2.2 Reaction-Diffusion Systems; 2.3 The One-Dimensional Wave Equation 2.4 Other Equations in Mathematical Physics3 Elliptic Boundary Value Problems; 3.1 Green's Formulas; 3.2 The Fundamental Solution of Laplace's Equation; 3.3 Mean Value Theorems for Harmonic Functions; 3.4 The Maximum Principle; 3.5 Uniqueness and Continuous Dependence on Data for the Dirichlet Problem; 3.6 Green's Function of the Dirichlet Problem; 3.7 Poisson's Formula; 3.8 Dirichlet's Principle; 3.9 The Generalized Solution of the Dirichlet Problem; 3.10 Abstract Fourier Series; 3.11 The Eigenvalues and Eigenfunctions of the Dirichlet Problem 3.12 The Case of Elliptic Equations in Divergence Form3.13 The Generalized Solution of the Neumann Problem; 3.14 Complements; 3.14.1 Harnack's Inequality; 3.14.2 Hopf's Maximum Principle; 3.14.3 The Newtonian Potential; 3.14.4 Perron's Method; 3.14.5 Layer Potentials; 3.14.6 Fredholm's Method of Integral Equations; 3.15 Problems; 4 Mixed Problems for Evolution Equations; 4.1 The Maximum Principle for the Heat Equation; 4.2 Vector-Valued Functions; 4.3 The Cauchy-Dirichlet Problem for the Heat Equation; 4.4 The Cauchy-Dirichlet Problem for the Wave Equation; 4.5 Problems 5 The Cauchy Problem for Evolution Equations5.1 The Fourier Transform; 5.1.1 The Fourier Transform on L1 (Rn); 5.1.2 Fourier Transform and Convolution; 5.1.3 The Fourier Transform on the Schwartz Space S (R"); 5.2 The Cauchy Problem for the Heat Equation; 5.3 The Cauchy Problem for the Wave Equation; 5.4 Nonhomogeneous Equations: Duhamel's Principle; 5.5 Problems; II Modern Theory; 6 Distributions; 6.1 The Fundamental Spaces of the Theory of Distributions; 6.2 Distributions: Examples; Operations with Distributions; 6.2.1 Regular Distributions; 6.2.2 The Dirac Distribution |
| ctrlnum | (OCoLC)826685105 |
| dewey-full | 515/.353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.353 |
| dewey-search | 515/.353 |
| dewey-sort | 3515 3353 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| series | De Gruyter textbook. |
| series2 | De Gruyter textbook |
| spelling | Precup, Radu. Linear and semilinear partial differential equations : an introduction / Radu Precup. Berlin ; Boston : De Gruyter, [2013] 1 online resource (xiv, 280 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier De Gruyter textbook Includes bibliographical references and index. Print version record. This textbook provides a brief and lucid introduction to the theory of linear partial differential equations. It clearly explains the transition from classical to generalized solutions and the natural way in which Sobolev spaces appear as completions of spaces of continuously differentiable functions. The solution operators associated to non-homogeneous equations are used to make transition to the theory of nonlinear PDEs. Organized on three parts, this material is suitable for three one-semester courses, a beginning one in the frame of classical analysis, a more advanced course in modern theo. Preface; Notation; I Classical Theory; 1 Preliminaries; 1.1 Basic Differential Operators; 1.2 Linear and Quasilinear Partial Differential Equations; 1.3 Solutions of Some Particular Equations; 1.4 Boundary Value Problems; 1.4.1 Boundary Value Problems for Poisson's Equation; 1.4.2 Boundary Value Problems for the Heat Equation; 1.4.3 Boundary Value Problems for the Wave Equation; 2 Partial Differential Equations and Mathematical Modeling; 2.1 Conservation Laws: Continuity Equations; 2.2 Reaction-Diffusion Systems; 2.3 The One-Dimensional Wave Equation 2.4 Other Equations in Mathematical Physics3 Elliptic Boundary Value Problems; 3.1 Green's Formulas; 3.2 The Fundamental Solution of Laplace's Equation; 3.3 Mean Value Theorems for Harmonic Functions; 3.4 The Maximum Principle; 3.5 Uniqueness and Continuous Dependence on Data for the Dirichlet Problem; 3.6 Green's Function of the Dirichlet Problem; 3.7 Poisson's Formula; 3.8 Dirichlet's Principle; 3.9 The Generalized Solution of the Dirichlet Problem; 3.10 Abstract Fourier Series; 3.11 The Eigenvalues and Eigenfunctions of the Dirichlet Problem 3.12 The Case of Elliptic Equations in Divergence Form3.13 The Generalized Solution of the Neumann Problem; 3.14 Complements; 3.14.1 Harnack's Inequality; 3.14.2 Hopf's Maximum Principle; 3.14.3 The Newtonian Potential; 3.14.4 Perron's Method; 3.14.5 Layer Potentials; 3.14.6 Fredholm's Method of Integral Equations; 3.15 Problems; 4 Mixed Problems for Evolution Equations; 4.1 The Maximum Principle for the Heat Equation; 4.2 Vector-Valued Functions; 4.3 The Cauchy-Dirichlet Problem for the Heat Equation; 4.4 The Cauchy-Dirichlet Problem for the Wave Equation; 4.5 Problems 5 The Cauchy Problem for Evolution Equations5.1 The Fourier Transform; 5.1.1 The Fourier Transform on L1 (Rn); 5.1.2 Fourier Transform and Convolution; 5.1.3 The Fourier Transform on the Schwartz Space S (R"); 5.2 The Cauchy Problem for the Heat Equation; 5.3 The Cauchy Problem for the Wave Equation; 5.4 Nonhomogeneous Equations: Duhamel's Principle; 5.5 Problems; II Modern Theory; 6 Distributions; 6.1 The Fundamental Spaces of the Theory of Distributions; 6.2 Distributions: Examples; Operations with Distributions; 6.2.1 Regular Distributions; 6.2.2 The Dirac Distribution Differential equations, Linear Textbooks. Differential equations, Partial Textbooks. MATHEMATICS Differential Equations Partial. bisacsh Differential equations, Linear fast Differential equations, Partial fast Textbooks fast has work: Linear and semilinear partial differential equations (Text) https://id.oclc.org/worldcat/entity/E39PCGcPKpvhXx9dXxgXvxCFw3 https://id.oclc.org/worldcat/ontology/hasWork Print version: 9783110269048 311026904X (DLC) 2012035431 De Gruyter textbook. |
| spellingShingle | Precup, Radu Linear and semilinear partial differential equations : an introduction / De Gruyter textbook. Preface; Notation; I Classical Theory; 1 Preliminaries; 1.1 Basic Differential Operators; 1.2 Linear and Quasilinear Partial Differential Equations; 1.3 Solutions of Some Particular Equations; 1.4 Boundary Value Problems; 1.4.1 Boundary Value Problems for Poisson's Equation; 1.4.2 Boundary Value Problems for the Heat Equation; 1.4.3 Boundary Value Problems for the Wave Equation; 2 Partial Differential Equations and Mathematical Modeling; 2.1 Conservation Laws: Continuity Equations; 2.2 Reaction-Diffusion Systems; 2.3 The One-Dimensional Wave Equation 2.4 Other Equations in Mathematical Physics3 Elliptic Boundary Value Problems; 3.1 Green's Formulas; 3.2 The Fundamental Solution of Laplace's Equation; 3.3 Mean Value Theorems for Harmonic Functions; 3.4 The Maximum Principle; 3.5 Uniqueness and Continuous Dependence on Data for the Dirichlet Problem; 3.6 Green's Function of the Dirichlet Problem; 3.7 Poisson's Formula; 3.8 Dirichlet's Principle; 3.9 The Generalized Solution of the Dirichlet Problem; 3.10 Abstract Fourier Series; 3.11 The Eigenvalues and Eigenfunctions of the Dirichlet Problem 3.12 The Case of Elliptic Equations in Divergence Form3.13 The Generalized Solution of the Neumann Problem; 3.14 Complements; 3.14.1 Harnack's Inequality; 3.14.2 Hopf's Maximum Principle; 3.14.3 The Newtonian Potential; 3.14.4 Perron's Method; 3.14.5 Layer Potentials; 3.14.6 Fredholm's Method of Integral Equations; 3.15 Problems; 4 Mixed Problems for Evolution Equations; 4.1 The Maximum Principle for the Heat Equation; 4.2 Vector-Valued Functions; 4.3 The Cauchy-Dirichlet Problem for the Heat Equation; 4.4 The Cauchy-Dirichlet Problem for the Wave Equation; 4.5 Problems 5 The Cauchy Problem for Evolution Equations5.1 The Fourier Transform; 5.1.1 The Fourier Transform on L1 (Rn); 5.1.2 Fourier Transform and Convolution; 5.1.3 The Fourier Transform on the Schwartz Space S (R"); 5.2 The Cauchy Problem for the Heat Equation; 5.3 The Cauchy Problem for the Wave Equation; 5.4 Nonhomogeneous Equations: Duhamel's Principle; 5.5 Problems; II Modern Theory; 6 Distributions; 6.1 The Fundamental Spaces of the Theory of Distributions; 6.2 Distributions: Examples; Operations with Distributions; 6.2.1 Regular Distributions; 6.2.2 The Dirac Distribution Differential equations, Linear Textbooks. Differential equations, Partial Textbooks. MATHEMATICS Differential Equations Partial. bisacsh Differential equations, Linear fast Differential equations, Partial fast |
| title | Linear and semilinear partial differential equations : an introduction / |
| title_auth | Linear and semilinear partial differential equations : an introduction / |
| title_exact_search | Linear and semilinear partial differential equations : an introduction / |
| title_full | Linear and semilinear partial differential equations : an introduction / Radu Precup. |
| title_fullStr | Linear and semilinear partial differential equations : an introduction / Radu Precup. |
| title_full_unstemmed | Linear and semilinear partial differential equations : an introduction / Radu Precup. |
| title_short | Linear and semilinear partial differential equations : |
| title_sort | linear and semilinear partial differential equations an introduction |
| title_sub | an introduction / |
| topic | Differential equations, Linear Textbooks. Differential equations, Partial Textbooks. MATHEMATICS Differential Equations Partial. bisacsh Differential equations, Linear fast Differential equations, Partial fast |
| topic_facet | Differential equations, Linear Textbooks. Differential equations, Partial Textbooks. MATHEMATICS Differential Equations Partial. Differential equations, Linear Differential equations, Partial Textbooks |
| work_keys_str_mv | AT precupradu linearandsemilinearpartialdifferentialequationsanintroduction |