Nonlinear Diffusion Equations

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Nonlinear diffusion equations, an important class of parabolic equations, come from a variety of diffusion phenomena which appear widely in nature. They are suggested as mathematical models of physical problems in many fields, such as filtration, ph…

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    Om Nonlinear Diffusion Equations

    Nonlinear diffusion equations, an important class of parabolic equations, come from a variety of diffusion phenomena which appear widely in nature. They are suggested as mathematical models of physical problems in many fields, such as filtration, phase transition, biochemistry and dynamics of biological groups. In many cases, the equations possess degeneracy or singularity. The appearance of degeneracy or singularity makes the study more involved and challenging. Many new ideas and methods have been developed to overcome the special difficulties caused by the degeneracy and singularity, which enrich the theory of partial differential equations.This book provides a comprehensive presentation of the basic problems, main results and typical methods for nonlinear diffusion equations with degeneracy. Some results for equations with singularity are touched upon.Contents: Newtonian Filtration Equations:Existence and Uniqueness of Solutions: One Dimensional CaseExistence and Uniqueness of Solutions: Higher Dimensional CaseRegularity of Solutions: One Dimensional CaseRegularity of Solutions: Higher Dimensional CaseProperties of the Free Boundary: One Dimensional CaseProperties of the Free Boundary: Higher Dimensional CaseInitial Trace of SolutionsOther ProblemsNon- Newtonian Filtration Equations:Existence of SolutionsHarnack Inequality and Initial Trace of SolutionsRegularity of SolutionsUniqueness of SolutionsProperties of the Free BoundaryOther ProblemsGeneral Quasilinear Equations of Second Order:Weakly Degenerate Equations in One DimensionWeakly Degenerate Equations in Higher DimensionStrongly Degenerate Equations in One DimensionDegenerate Equations in Higher Dimension without Terms of Lower OrderGeneral Strongly Degenerate Equations in Higher DimensionClasses BV and BVxNonlinear Diffusion Equations of Higher Order:Similarity Solutions of a Fourth Order EquationEquations with Double-DegeneracyCahn–Hilliard Equation with Constant MobilityCahn–Hilliard Equations with Positive Concentration Dependent MobilityThin Film EquationCahn–Hilliard Equation with Degenerate MobilityReadership: Researchers, lecturers and graduate students in the fields of analysis and differential equations, mathematical physics and fluid mechanics.Key Features:The voluminous research reported in this book demonstrates that positive learning environments lead to valuable improvements in student achievement and attitudesThis book not only traces the remarkable expansion of the field of learning environments internationally, but it also provides a unique focus on the distinctive contributions made by researchers around the worldThis book demonstrates why the learning environment should not be ignored by those wishing to improve the effectiveness of schools and universities

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    Detaljer

    Format
    E-Bok
    Filformat
    PDF
    Utgivelsesår
    2001
    Forlag
    World Scientific Publishing Co
    Språk
    Engelsk
    ISBN
    9789812799791
    Sider
    520

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