Nonlinear diffusion equations

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Nonlinear diffusion equations / Zhuoqun Wu ... [et al.]

資料種別:

図書

出版情報:

Singapore : World Scientific, c2001

形態:

xvii, 502 p. ; 23 cm

著者名:

ISBN:

9789810247188 [9810247184]

書誌ID:

BA54696489

子書誌情報

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書誌詳細

注記:

Includes bibliographical references (p. 479-502)

主題:

非線型微分方程式

言語:

英語

目次情報:

Preface

Newtonian Filtration Equations / Chapter 1：

Introduction / 1.1：

Physical examples / 1.1.1：

Definitions of generalized solutions / 1.1.2：

Special solutions / 1.1.3：

Existence and Uniqueness of Solutions: One Dimensional Case / 1.2：

Uniqueness of solutions / 1.2.1：

Existence of solutions / 1.2.2：

Comparison theorems / 1.2.3：

Some extensions / 1.2.4：

Existence and Uniqueness of Solutions: Higher Dimensional Case / 1.3：

Comparison theorem and uniqueness of solutions / 1.3.1：

Regularity of Solutions: One Dimensional Case / 1.3.2：

Lemma / 1.4.1：

Regularity of solutions / 1.4.2：

Regularity of Solutions: Higher Dimensional Case / 1.4.3：

Generalized class B[subscript 2] / 1.5.1：

Some lemmas / 1.5.2：

Properties of functions in the generalized class B[subscript 2] / 1.5.3：

Holder continuity of solutions / 1.5.4：

Properties of the Free Boundary: One Dimensional Case / 1.6：

Finite propagation of disturbances / 1.6.1：

Localization and extinction of disturbances / 1.6.2：

Differential equation on the free boundary / 1.6.3：

Continuously differentiability of the free boundary / 1.6.4：

Some further results / 1.6.5：

Properties of the Free Boundary: Higher Dimensional Case / 1.7：

Monotonicity and Holder continuity of the free boundary / 1.7.1：

Lipschitz continuity of the free boundary / 1.7.2：

Initial Trace of Solutions / 1.7.3：

Harnack inequality / 1.8.1：

Main result / 1.8.2：

Extension of existence and uniqueness theorem / 1.8.3：

Other Problems / 1.9：

Equations with strongly nonlinear sources / 1.9.1：

Asymptotic properties of solutions / 1.9.2：

Non-Newtonian Filtration Equations / Chapter 2：

Introduction Preliminary Knowledge / 2.1：

Introduction Physical example / 2.1.1：

Basic spaces and some lemmas / 2.1.2：

Existence of Solutions / 2.1.3：

The case u[subscript 0] [set membership] C[superscript [infinity] subscript 0](R[superscript N]) or u[subscript 0] [set membership] L[superscript 1](R[superscript N]) [intersection of] L[superscript [infinity](R[superscript N]) / 2.2.1：

The case u[subscript 0] [set membership] L[superscript 1 subscript loc](R[superscript N]) / 2.2.2：

Some remarks / 2.2.3：

Harnack Inequality and the Initial Trace of Solutions / 2.3：

Local Harnack inequality / 2.3.1：

Global Harnack inequality / 2.3.2：

Initial trace of solutions / 2.3.3：

Regularity of Solutions / 2.4：

Boundedness of solutions / 2.4.1：

Boundedness of the gradient of solutions / 2.4.2：

Holder continuity of the gradient of solutions / 2.4.3：

Uniqueness of Solutions / 2.5：

Auxiliary propositions / 2.5.1：

Uniqueness theorem and its proof / 2.5.2：

Properties of the Free Boundary / 2.6：

p-Laplacian equation with strongly nonlinear sources / 2.6.1：

General Quasilinear Equations of Second Order / 2.7.2：

Weakly Degenerate Equations in One Dimension / 3.1：

Uniqueness of bounded and measurable solutions / 3.2.1：

Existence of continuous solutions / 3.2.2：

Weakly Degenerate Equations in Higher Dimension / 3.2.3：

Existence of continuous solutions for equations with two points of degeneracy / 3.3.1：

Uniqueness of BV solutions / 3.3.2：

Existence of BV solutions / 3.3.3：

Strongly Degenerate Equations in One Dimension / 3.3.4：

Definitions of solutions with discontinuity / 3.4.1：

Interior discontinuity condition / 3.4.2：

Uniqueness of BV solutions of the Cauchy problem / 3.4.3：

Formulation of the boundary value problem / 3.4.4：

Boundary discontinuity condition / 3.4.5：

Uniqueness of BV solutions of the first boundary value problem / 3.4.6：

Existence of BV solutions of the first boundary value problem / 3.4.7：

Equations with degeneracy at infinity / 3.4.8：

Properties of the curves of discontinuity / 3.4.10：

Degenerate Equations in Higher Dimension without Terms of Lower Order / 3.5：

Uniqueness of bounded and integrable solutions / 3.5.1：

A lemma on weak convergence / 3.5.2：

General Strongly Degenerate Equations in Higher Dimension / 3.5.3：

Appendix Classes BV and BV[subscript x] / 3.6.1：

Nonlinear Diffusion Equations of Higher Order / Chapter 4：

Similarity Solutions of a Fourth Order Equation / 4.1：

Definition of similarity solutions / 4.2.1：

Existence and uniqueness of global solutions of the Cauchy problem / 4.2.2：

Properties of solutions at zero points / 4.2.3：

Properties of unbounded solutions / 4.2.5：

Bounded solutions on the half line / 4.2.6：

Bounded solutions on the whole line / 4.2.7：

Properties of solutions in typical cases k = 1,2,3,4 / 4.2.8：

Behavior of similarity solutions as t [right arrow] 0[superscript +] / 4.2.9：

Equations with Double-Degeneracy / 4.3：

Weighted energy equality of solutions / 4.3.1：

Some auxiliary inequalities / 4.3.4：

Asymptotic behavior of solutions / 4.3.5：

Extinction of solutions at finite time / 4.3.7：

Nonexistence of nonnegative solutions / 4.3.8：

Infinite propagation case / 4.3.9：

Cahn-Hilliard Equation with Constant Mobility / 4.4：

Existence of classical solutions / 4.4.1：

Blowing-up of solutions / 4.4.2：

Global existence of solutions for small initial value / 4.4.3：

Cahn-Hilliard Equations with Positive Concentration Dependent Mobility / 4.5：

A modified Campanato space / 4.5.1：

Holder norm estimates for a linear problem / 4.5.2：

Zero potential case / 4.5.3：

General case / 4.5.4：

Thin Film Equation / 4.6：

Definition of generalized solutions / 4.6.1：

Approximate solutions / 4.6.2：

Nonnegativity of solutions / 4.6.3：

Zeros of nonnegative solutions / 4.6.5：

Monotonicity of the support of solutions / 4.6.6：

Cahn-Hilliard Equation with Degenerate Mobility / 4.7：

Models with degenerate mobility / 4.7.1：

Definition of physical solutions / 4.7.2：

Physical solutions / 4.7.3：

Bibliography

Preface

Newtonian Filtration Equations / Chapter 1：

Introduction / 1.1：

Physical examples / 1.1.1：

Definitions of generalized solutions / 1.1.2：

Special solutions / 1.1.3：

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