Frederick Bloom SIAM Studies in Applied Mathematics 3
Examines illposed, initialhistory boundaryvalue problems associated with systems of partialintegrodifferential equations arising in linear and nonlinear theories of mechanical viscoelasticity, rigid nonconducting material dielectrics, and heat conductors with memory.
Variants of two differential inequalities, logarithmic convexity, and concavity are employed. Ideas based on energy arguments, Riemann invariants, and topological dynamics applied to evolution equations are also introduced. These concepts are discussed in an introductory chapter and applied there to initial boundary value problems of linear and nonlinear diffusion and elastodynamics. Subsequent chapters begin with an explanation of the underlying physical theories.
Contents
IllPosed Initial BoundaryValue Problems in Mathematical Physics: Examples of the Basic Logarithmic Convexity and Concavity Arguments for PDE; IllPosed Problems for the PartialIntegrodifferential Equations of Linear and Nonlinear Viscoelasticity; IllPosed Problems for Some Integrodifferential Equations of Electromagnetic Theory; Some Recent Directions in Research on Nonlinear Integrodifferential Equations.
1981 / ix + 222 pages / Hardcover / ISBN13: 9780898711714 / ISBN10: 0898711711 / List Price $96.00 / SIAM Member Price $67.20 / Order Code AM03
