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Smoothing and Decay Estimates for Nonlinear Diffusion Equations: Equations of Porous Medium Type

Juan Luis Vázquez

Published in print:
2006
Published Online:
September 2007
ISBN:
9780199202973
eISBN:
9780191707919
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199202973.001.0001
Subject:
Mathematics, Applied Mathematics

This book is concerned with the quantitative aspects of the theory of nonlinear diffusion equations; equations which can be seen as nonlinear variations of the classical heat equation. They appear as ... More


Annuity demand theory

Edmund Cannon and Ian Tonks

in Annuity Markets

Published in print:
2008
Published Online:
January 2009
ISBN:
9780199216994
eISBN:
9780191711978
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199216994.003.0007
Subject:
Business and Management, Pensions and Pension Management

This chapter discusses Yaari's (19665) annuitization result, which states that a risk-averse individual concerned about longevity risk (uncertain length of life) will always purchase actuarially-fair ... More


Smoothness and Asymptotic Smoothness

Joram Lindenstrauss, David Preiss, and Tiˇser Jaroslav

in Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces (AM-179)

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691153551
eISBN:
9781400842698
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153551.003.0008
Subject:
Mathematics, Analysis

This chapter describes the modulus of smoothness of a function in the direction of a family of subspaces and the much simpler notion of upper Fréchet differentiability. It also considers the notion ... More


Bayesian Smoothing and Regression for Longitudinal, Spatial and Event History Data

Ludwig Fahrmeir and Thomas Kneib

Published in print:
2011
Published Online:
September 2011
ISBN:
9780199533022
eISBN:
9780191728501
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199533022.001.0001
Subject:
Mathematics, Probability / Statistics, Biostatistics

Several recent advances in smoothing and semiparametric regression are presented in this book from a unifying, Bayesian perspective. Simulation-based full Bayesian Markov chain Monte Carlo (MCMC) ... More


Searching for Structure in Point Data

Željko Ivezi, Andrew J. Connolly, Jacob T. VanderPlas, Alexander Gray, Željko Ivezi, Andrew J. Connolly, Jacob T. VanderPlas, and Alexander Gray

in Statistics, Data Mining, and Machine Learning in Astronomy: A Practical Python Guide for the Analysis of Survey Data

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691151687
eISBN:
9781400848911
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691151687.003.0006
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

Inferring the probability density function (pdf) from a sample of data is known as density estimation. The same methodology is often called data smoothing. Density estimation in the one-dimensional ... More


Between Scylla and Charybdis: Improving the Cost Effectiveness of Public Pension Retirement Plans

M. Barton Waring

in The Future of Public Employee Retirement Systems

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199573349
eISBN:
9780191721946
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199573349.003.0004
Subject:
Business and Management, Public Management, Pensions and Pension Management

Unless defined benefit pension plans are managed much better and more cost-effectively, they will be replaced by defined contribution plans. Benefit and contribution policies need to be carefully ... More


Spatial variation in risk

Dirk U. Pfeiffer, Timothy P. Robinson, Mark Stevenson, Kim B. Stevens, David J. Rogers, and Archie C. A. Clements

in Spatial Analysis in Epidemiology

Published in print:
2008
Published Online:
September 2008
ISBN:
9780198509882
eISBN:
9780191709128
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198509882.003.0006
Subject:
Biology, Disease Ecology / Epidemiology

This chapter discusses spatial variation in risk. Epidemiological disease investigations should include an assessment of the spatial variation of disease risk, as this may provide important clues ... More


Absent Hair

Susan Niditch

in "My Brother Esau Is a Hairy Man": Hair and Identity in Ancient Israel

Published in print:
2008
Published Online:
May 2008
ISBN:
9780195181142
eISBN:
9780199869671
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195181142.003.0005
Subject:
Religion, Judaism

This chapter explores a set of biblical texts dealing with the loss or absence of hair: the tale of David's envoys in 2 Samuel 10:4–5; related texts concerning conquest and images of shaving; ... More


The Pharmacology of Vascular Smooth Muscle

C. J. Garland and J. A. Angus (eds)

Published in print:
1996
Published Online:
March 2012
ISBN:
9780192623874
eISBN:
9780191724671
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780192623874.001.0001
Subject:
Neuroscience, Sensory and Motor Systems

This book provides an understanding of how events at the cellular level impact on the cardiovascular system as a whole. Advances in knowledge are highlighted and all the themes are presented from the ... More


DIFFUSION EQUATION

George Em Karniadakis and Spencer J. Sherwin

in Spectral/hp Element Methods for Computational Fluid Dynamics

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198528692
eISBN:
9780191713491
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528692.003.0005
Subject:
Mathematics, Numerical Analysis

This chapter considers the diffusion equation: an implicit in time discretization leads to the Helmholtz equation. Both the temporal discretization and eigenspectra of second-order operators that ... More


INTRODUCTION

Terry Lyons and Zhongmin Qian

in System Control and Rough Paths

Published in print:
2002
Published Online:
September 2007
ISBN:
9780198506485
eISBN:
9780191709395
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198506485.003.0001
Subject:
Mathematics, Probability / Statistics

The concept of a differential equation controlled by a rough path can be motivated by quite simple examples. One such example is a linear system driven by two-dimensional noise. This example is ... More


Numerical Simulation Of Microflows And Nanoflows

Narayan R. Aluru and George Em Karniadakis

in Micro/Nano Technology Systems for Biomedical Applications: Microfluidics, Optics, and Surface Chemistry

Published in print:
2010
Published Online:
September 2010
ISBN:
9780199219698
eISBN:
9780191594229
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199219698.003.0003
Subject:
Mathematics, Mathematical Biology

In this chapter we review recent advances in numerical simulation of micro and nanoflows. For coarse-grained simulation of microfuidics, we present an overview of Lattice Boltzmann, Brownian ... More


Working with roots

Christopher G. Small and Jinfang Wang

in Numerical Methods for Nonlinear Estimating Equations

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198506881
eISBN:
9780191709258
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198506881.003.0004
Subject:
Mathematics, Probability / Statistics

This chapter studies the broad class of models which have difficult problems of nonlinearity and multiple roots. These models include the mixture models, a model for bivariate normal paired data with ... More


Superfast FDE

Juan Luis Vázquez

in Smoothing and Decay Estimates for Nonlinear Diffusion Equations: Equations of Porous Medium Type

Published in print:
2006
Published Online:
September 2007
ISBN:
9780199202973
eISBN:
9780191707919
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199202973.003.0010
Subject:
Mathematics, Applied Mathematics

This chapter addresses the question of extending the theory and estimates of the FDE to cover the singular range m ≤ 0, that has only been partially considered in previous chapters. This completes ... More


Evolution equations of the p-Laplacian type

Juan Luis Vázquez

in Smoothing and Decay Estimates for Nonlinear Diffusion Equations: Equations of Porous Medium Type

Published in print:
2006
Published Online:
September 2007
ISBN:
9780199202973
eISBN:
9780191707919
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199202973.003.0012
Subject:
Mathematics, Applied Mathematics

This chapter presents the application of the foregoing ideas to the p-Laplacian evolution equation and the doubly nonlinear evolution equation. Topics covered include the doubly linear diffusion ... More


Introduction

Juan Luis Vázquez

in Smoothing and Decay Estimates for Nonlinear Diffusion Equations: Equations of Porous Medium Type

Published in print:
2006
Published Online:
September 2007
ISBN:
9780199202973
eISBN:
9780191707919
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199202973.003.0001
Subject:
Mathematics, Applied Mathematics

This introductory chapter opens with an explanation of the purpose of the book, which is to obtain basic estimates for some particular nonlinear parabolic equations and to derive consequences about ... More


Smoothing effect and time decay. Data in L 1 (R n ) or M (R n )

Juan Luis Vázquez

in Smoothing and Decay Estimates for Nonlinear Diffusion Equations: Equations of Porous Medium Type

Published in print:
2006
Published Online:
September 2007
ISBN:
9780199202973
eISBN:
9780191707919
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199202973.003.0003
Subject:
Mathematics, Applied Mathematics

This chapter discusses the smoothing and decay effects for the porous medium equation, using as a model case the famous Barenblatt solutions that have explicit formulas. Topics covered include ... More


Smoothing effect and time decay from L p or M p

Juan Luis Vázquez

in Smoothing and Decay Estimates for Nonlinear Diffusion Equations: Equations of Porous Medium Type

Published in print:
2006
Published Online:
September 2007
ISBN:
9780199202973
eISBN:
9780191707919
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199202973.003.0004
Subject:
Mathematics, Applied Mathematics

This chapter addresses the question of boundedness for the same equation when the initial data are chosen in the Lebesgue space Lp, p Ɛ (1, ∞). It is assumed that m > mc . The ... More


Subcritical range of the FDE. Critical line. Extinction. Backward effect

Juan Luis Vázquez

in Smoothing and Decay Estimates for Nonlinear Diffusion Equations: Equations of Porous Medium Type

Published in print:
2006
Published Online:
September 2007
ISBN:
9780199202973
eISBN:
9780191707919
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199202973.003.0006
Subject:
Mathematics, Applied Mathematics

This chapter studies the smoothing effect and decay rates for the FDE in the subcritical range m < mc , and also for the critical exponent mc = (n - 2)/n. ... More


Logarithmic diffusion in 2D and intermediate 1D range

Juan Luis Vázquez

in Smoothing and Decay Estimates for Nonlinear Diffusion Equations: Equations of Porous Medium Type

Published in print:
2006
Published Online:
September 2007
ISBN:
9780199202973
eISBN:
9780191707919
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199202973.003.0009
Subject:
Mathematics, Applied Mathematics

This chapter studies two transition situations where non-uniqueness plays an important role. The first deals with the range -1 < m ≤ 0 in n = 1, which looks like supercritical but contains the ... More


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