Nonlinear reaction-diffusion-convection equations : Lie and conditional symmetry, exact solutions, and their applications

Content: \"\"Cover\"\"
 \"\"Title \"\"
 \"\"Series Editors\"\"
 \"\"copyright\"\"
 \"\"Contents\"\"
 \"\"Preface\"\"
 \"\"List of Figures\"\"
 \"\"List of Tables\"\"
 \"\"Acronyms\"\"
 \"\"Chapter 1 Introduction\"\"
 \"\"1.1 Nonlinear reaction-diffusion-convection equations in mathematical modeling\"\"
 \"\"1.2 Main methods for exact solving nonlinear reaction-diffusion- convection equations\"\"
 \"\"1.3 Lie symmetry of differential equations: historical review, definitions and properties\"\"
 \"\"Chapter 2 Lie symmetries of reaction-diffusion-convection equations\"\"
 \"\"2.1 Symmetry of the linear diffusion equation\"\" \"\"2.2 Symmetry of the nonlinear diffusion equation\"\"\"\"2.3 Equivalence transformations and form-preserving transformations\"\"
 \"\"2.3.1 The group of equivalence transformations\"\"
 \"\"2.3.2 Form-preserving transformations\"\"
 \"\"2.4 Determining equations for reaction-diffusion-convection equations\"\"
 \"\"2.5 Complete description of Lie symmetries of reaction-diffusion-convection equations\"\"
 \"\"2.5.1 Principal algebra of invariance\"\"
 \"\"2.5.2 Necessary conditions for nontrivial Lie symmetry\"\"
 \"\"2.5.3 Lie symmetry classification via the Lieâ#x80
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Ovsiannikov algorithm\"\" \"\"2.5.4 Application of form-preserving transformation\"\"\"\"2.6 Nonlinear equations arising in applications and their Lie symmetry\"\"
 \"\"2.6.1 Heat (diffusion) equations with power-law nonlinearity\"\"
 \"\"2.6.2 Diffusion equations with a convective term\"\"
 \"\"2.6.3 Nonlinear equations describing three types of transport mechanisms\"\"
 \"\"Chapter 3 Conditional symmetries of reaction-diffusion-convection equations\"\"
 \"\"3.1 Conditional symmetry of differential equations: historical re-view, definitions and properties\"\"
 \"\"3.2 Qâ#x80
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conditional symmetry of the nonlinear heat equation\"\" \"\"3.3 Determining equations for finding Q-conditional symmetry of reaction-diffusion-convection equations\"\"\"\"3.4 Qâ#x80
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conditional symmetry of reaction-diffusion-convection equations with constant diffusivity\"\"
 \"\"3.5 Qâ#x80
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conditional symmetry of reaction-diffusion-convection equa-tions with power-law diffusivity\"\"
 \"\"3.5.1 The case of proportional diffusion and convection coef-ficients\"\"
 \"\"3.5.2 The case of different diffusion and convection coeffi-cients\"\"
 \"\"3.6 Qâ#x80
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conditional symmetry of reaction-diffusion-convection equations with exponential diffusivity\"\" \"\"3.6.1 Solving the nonlinear system (3.166)\"\"\"\"3.6.2 Solving the nonlinear system (3.169)\"\"
 \"\"3.7 Nonlinear equations arising in applications and their conditional symmetry\"\"
 \"\"Chapter 4 Exact solutions of reaction-diffusion-convection equations and their applications\"\"
 \"\"4.1 Classification of exact solutions from the symmetry point of view\"\"
 \"\"4.2 Examples of exact solutions for some well-known nonlinear equations\"\"
 \"\"4.3 Solutions of some reaction-diffusion-convection equations arising in biomedical applications\"\"
 \"\"4.3.1 The Fisher and Murray equations\"\" \"\"4.3.2 The Fitzhughâ#x80
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Nagumo equation and its generalizations\"\"