An Introduction to Nonlinear Partial Differential EquationsWhile outstanding treatises on nonlinear partial differential equations do exist, beginning students seeking a fundamental understanding of their nature and application generally find these approaches to be too advanced. David Logan's new text, the outgrowth of his many years as a professor at the University of Nebraska, resolves the dilemma by providing upper-level and graduate students in mathematics, engineering, and the physical sciences with a sensibly straightforward introduction to nonlinear PDEs, striking a balance between the mathematical and physical aspects of the subject. An Introduction to Nonlinear Partial Differential Equations covers a wide range of applications, including biology, chemistry, porous media, combustion, detonation, traffic flow, water waves, plug flow reactors, and heat transfer, among other topics in applied mathematics. Flexible enough to enable instructors to adapt portions of the book to their own curricula, An Introduction to Nonlinear Partial Differential Equations works effectively in first courses on nonlinear PDEs, second course on PDEs, and in advanced applied mathematics classes that emphasize modeling. |
Contents
First Order Equations and Characteristics | 51 |
Weak Solutions to Hyperbolic Equations | 80 |
Diffusion Processes | 126 |
Copyright | |
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An Introduction to Nonlinear Partial Differential Equations J. David Logan No preview available - 2008 |
Common terms and phrases
assume assumption asymptotic boundary conditions boundary value problem Burgers called characteristic diagram chemical reaction coefficient combustion conservation law Consider the initial continuous functions critical point curve defined denote density derivatives determine detonation diffusion equation dimensionless discontinuity domain Duxx eigenvalues elliptic energy equilibrium example EXERCISES existence Fisher's equation flow fluid flux gas dynamics given gradient h₁ heat Hugoniot hyperbolic inequality initial condition initial value problem integral invariant jump conditions linear mass mathematical matrix maximum principle method momentum norm obtain orbit ordinary differential equation P₁ parameter partial differential equations perturbation piston positive constant propagated reaction-diffusion equations region satisfies Section shallow water equations shown in Figure smooth solve spacetime species speed temperature term theorem transformation traveling wave solutions u₁ unique v₁ variables vector velocity wavefront zero