{"product_id":"nonlinear-pdes-2e-pure-and-applied-mathematics-a-wiley-series-of-texts-monographs-and-tracts-9780470225950","title":"Nonlinear PDEs 2e Pure and Applied Mathematics A","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis  introductory textbook on nonlinear partial differential equations is technique oriented with an emphasis on  applications and  is designed to build a foundation for studying advanced treatises in the field. The Second Edition features an updated bibliography as well as an increase in the number of exercises.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"This book is an ideal text for applied mathematics courses at the upper-undergraduate and graduate levels. It also serves as a valuable resource for researchers and professionals in the fields of mathematics, biology, engineering, and physics who would like to further their knowledge of PDEs.\" (\u003ci\u003eMathematical Reviews\u003c\/i\u003e, 2009c)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface xi\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1. Introduction to Partial Differential Equations 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Partial Differential Equations 2\u003c\/p\u003e \u003cp\u003e1.1.1 Equations and Solutions 2\u003c\/p\u003e \u003cp\u003e1.1.2 Classification 5\u003c\/p\u003e \u003cp\u003e1.1.3 Linear versus Nonlinear 8\u003c\/p\u003e \u003cp\u003e1.1.4 Linear Equations 11\u003c\/p\u003e \u003cp\u003e1.2 Conservation Laws 20\u003c\/p\u003e \u003cp\u003e1.2.1 One Dimension 20\u003c\/p\u003e \u003cp\u003e1.2.2 Higher Dimensions 23\u003c\/p\u003e \u003cp\u003e1.3 Constitutive Relations 25\u003c\/p\u003e \u003cp\u003e1.4 Initial and Boundary Value Problems 35\u003c\/p\u003e \u003cp\u003e1.5 Waves 45\u003c\/p\u003e \u003cp\u003e1.5.1 Traveling Waves 45\u003c\/p\u003e \u003cp\u003e1.5.2 Plane Waves 50\u003c\/p\u003e \u003cp\u003e1.5.3 Plane Waves and Transforms 52\u003c\/p\u003e \u003cp\u003e1.5.4 Nonlinear Dispersion 54\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2. First-Order Equations and Characteristics 61\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Linear First-Order Equations 62\u003c\/p\u003e \u003cp\u003e2.1.1 Advection Equation 62\u003c\/p\u003e \u003cp\u003e2.1.2 Variable Coefficients 64\u003c\/p\u003e \u003cp\u003e2.2 Nonlinear Equations 68\u003c\/p\u003e \u003cp\u003e2.3 Quasilinear Equations 72\u003c\/p\u003e \u003cp\u003e2.3.1 The General Solution 76\u003c\/p\u003e \u003cp\u003e2.4 Propagation of Singularities 81\u003c\/p\u003e \u003cp\u003e2.5 General First-Order Equation 86\u003c\/p\u003e \u003cp\u003e2.5.1 Complete Integral 91\u003c\/p\u003e \u003cp\u003e2.6 A Uniqueness Result 94\u003c\/p\u003e \u003cp\u003e2.7 Models in Biology 96\u003c\/p\u003e \u003cp\u003e2.7.1 Age Structure 96\u003c\/p\u003e \u003cp\u003e2.7.2 Structured Predator-Prey Model 101\u003c\/p\u003e \u003cp\u003e2.7.3 Chemotherapy 103\u003c\/p\u003e \u003cp\u003e2.7.4 Mass Structure 105\u003c\/p\u003e \u003cp\u003e2.7.5 Size-Dependent Predation 106\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3. Weak Solutions to Hyperbolic Equations 113\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Discontinuous Solutions 114\u003c\/p\u003e \u003cp\u003e3.2 Jump Conditions 116\u003c\/p\u003e \u003cp\u003e3.2.1 Rarefaction Waves 118\u003c\/p\u003e \u003cp\u003e3.2.2 Shock Propagation 119\u003c\/p\u003e \u003cp\u003e3.3 Shock Formation 125\u003c\/p\u003e \u003cp\u003e3.4 Applications 131\u003c\/p\u003e \u003cp\u003e3.4.1 Traffic Flow 132\u003c\/p\u003e \u003cp\u003e3.4.2 Plug Flow Chemical Reactors 136\u003c\/p\u003e \u003cp\u003e3.5 Weak Solutions: A Formal Approach 140\u003c\/p\u003e \u003cp\u003e3.6 Asymptotic Behavior of Shocks 148\u003c\/p\u003e \u003cp\u003e3.6.1 Equal-Area Principle 148\u003c\/p\u003e \u003cp\u003e3.6.2 Shock Fitting 152\u003c\/p\u003e \u003cp\u003e3.6.3 Asymptotic Behavior 154\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4. Hyperbolic Systems 159\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Shallow-Water Waves: Gas Dynamics 160\u003c\/p\u003e \u003cp\u003e4.1.1 Shallow-Water Waves160\u003c\/p\u003e \u003cp\u003e4.1.2 Small-Amplitude Approximation 163\u003c\/p\u003e \u003cp\u003e4.1.3 Gas Dynamics 164\u003c\/p\u003e \u003cp\u003e4.2 Hyperbolic Systems and Characteristics 169\u003c\/p\u003e \u003cp\u003e4.2.1 Classification 170\u003c\/p\u003e \u003cp\u003e4.3 The Riemann Method 179\u003c\/p\u003e \u003cp\u003e4.3.1 Jump Conditions for Systems 179\u003c\/p\u003e \u003cp\u003e4.3.2 Breaking Dam Problem 181\u003c\/p\u003e \u003cp\u003e4.3.3 Receding Wall Problem 183\u003c\/p\u003e \u003cp\u003e4.3.4 Formation of a Bore 187\u003c\/p\u003e \u003cp\u003e4.3.5 Gas Dynamics 190\u003c\/p\u003e \u003cp\u003e4.4 Hodographs and Wavefronts 192\u003c\/p\u003e \u003cp\u003e4.4.1 Hodograph Transformation 192\u003c\/p\u003e \u003cp\u003e4.4.2 Wavefront Expansions 193\u003c\/p\u003e \u003cp\u003e4.5 Weakly Nonlinear Approximations 201\u003c\/p\u003e \u003cp\u003e4.5.1 Derivation of Burgers‘ Equation 202\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5.\u003c\/b\u003e Diffusion Processes 209\u003c\/p\u003e \u003cp\u003e5.1 Diffusion and Random Motion 210\u003c\/p\u003e \u003cp\u003e5.2 Similarity Methods 217\u003c\/p\u003e \u003cp\u003e5.3 Nonlinear Diffusion Models 224\u003c\/p\u003e \u003cp\u003e5.4 Reaction-Diffusion: Fisher’s Equation 234\u003c\/p\u003e \u003cp\u003e5.4.1 Traveling Wave Solutions 235\u003c\/p\u003e \u003cp\u003e5.4.2 Perturbation Solution 238\u003c\/p\u003e \u003cp\u003e5.4.3 Stability of Traveling Waves 240\u003c\/p\u003e \u003cp\u003e5.4.4 Nagumo‘s Equation 242\u003c\/p\u003e \u003cp\u003e5.5 Advection-Diffusion: Burgers’ Equation 245\u003c\/p\u003e \u003cp\u003e5.5.1 Traveling Wave Solution 246\u003c\/p\u003e \u003cp\u003e5.5.2 Initial Value Problem 247\u003c\/p\u003e \u003cp\u003e5.6 Asymptotic Solution to Burgers’ Equation 250\u003c\/p\u003e \u003cp\u003e5.6.1 Evolution of a Point Source 252\u003c\/p\u003e \u003cp\u003eAppendix: Dynamical Systems 257\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6. Reaction-Diffusion Systems 267\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Reaction-Diffusion Models 268\u003c\/p\u003e \u003cp\u003e6.1.1 Predator-Prey Model 270\u003c\/p\u003e \u003cp\u003e6.1.2 Combustion 271\u003c\/p\u003e \u003cp\u003e6.1.3 Chemotaxis 274\u003c\/p\u003e \u003cp\u003e6.2 Waveling IJ1Bve Solutions 277\u003c\/p\u003e \u003cp\u003e6.2.1 Model for the Spread of a Disease 278\u003c\/p\u003e \u003cp\u003e6.2.2 Contaminant Transport in Groundwater 284\u003c\/p\u003e \u003cp\u003e6.3 Existence of Solutions 292\u003c\/p\u003e \u003cp\u003e6.3.1 Fixed-Point Iteration 293\u003c\/p\u003e \u003cp\u003e6.3.2 Semilinear Equations 297\u003c\/p\u003e \u003cp\u003e6.3.3 Normed Linear Spaces 300\u003c\/p\u003e \u003cp\u003e6.3.4 General Existence Theorem 303\u003c\/p\u003e \u003cp\u003e6.4 Maximum Principles and Comparison Theorems 309\u003c\/p\u003e \u003cp\u003e6.4.1 Maximum Principles 309\u003c\/p\u003e \u003cp\u003e6.4.2 Comparison Theorems 314\u003c\/p\u003e \u003cp\u003e6.5 Energy Estimates and Asymptotic Behavior 317\u003c\/p\u003e \u003cp\u003e6.5.1 Calculus Inequalities 318\u003c\/p\u003e \u003cp\u003e6.5.2 Energy Estimates 320\u003c\/p\u003e \u003cp\u003e6.5.3 Invariant Sets 326\u003c\/p\u003e \u003cp\u003e6.6 Pattern Formation 333\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7. Equilibrium Models 345\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Elliptic Models 346\u003c\/p\u003e \u003cp\u003e7.2 Theoretical Results 352\u003c\/p\u003e \u003cp\u003e7.2.1 Maximum Principle 353\u003c\/p\u003e \u003cp\u003e7.2.2 Existence Theorem 355\u003c\/p\u003e \u003cp\u003e7.3 Eigenvalue Problems 358\u003c\/p\u003e \u003cp\u003e7.3.1 Linear Eigenvalue Problems 358\u003c\/p\u003e \u003cp\u003e7.3.2 Nonlinear Eigenvalue Problems 361\u003c\/p\u003e \u003cp\u003e7.4 Stability and Bifurcation 364\u003c\/p\u003e \u003cp\u003e7.4.1 Ordinary Differential Equations 364\u003c\/p\u003e \u003cp\u003e7.4.2 Partial Differential Equations 368\u003c\/p\u003e \u003cp\u003eReferences 387\u003c\/p\u003e \u003cp\u003eIndex 395\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402305446231,"sku":"9780470225950","price":111.56,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780470225950.jpg?v=1730480009","url":"https:\/\/bookcurl.com\/products\/nonlinear-pdes-2e-pure-and-applied-mathematics-a-wiley-series-of-texts-monographs-and-tracts-9780470225950","provider":"Book Curl","version":"1.0","type":"link"}