A unifying perspective on linear continuum equations prevalent in science. Part II: Canonical forms for time-harmonic equations
arXiv:2006.02433
Abstract
Following some past advances, we reformulate a large class of linear continuum science equations in the format of the extended abstract theory of composites so that we can apply this theory to better understand and efficiently solve those equations. Here in part II we elucidate the form for many time-harmonic equations that do not involve higher order gradients.
24 pages, 2 figures, What were called the Milton-Briane-Willis equations are now, more correctly, called the local Willis equations
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- A unifying perspective on linear continuum equations prevalent in science. Part III: Canonical forms for dynamic equations with moduli that may, or may not, vary with time
- A unifying perspective on linear continuum equations prevalent in science. Part IV: Canonical forms for equations involving higher order gradients
- A unifying perspective on linear continuum equations prevalent in science. Part I: Canonical forms for static, steady, and quasistatic equations
- A unifying perspective on linear continuum equations prevalent in science. Part VI: rapidly converging series expansions for their solution
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Cited by in corpus (4)
- A unifying perspective on linear continuum equations prevalent in science. Part I: Canonical forms for static, steady, and quasistatic equations
- A unifying perspective on linear continuum equations prevalent in science. Part III: Canonical forms for dynamic equations with moduli that may, or may not, vary with time
- A unifying perspective on linear continuum equations prevalent in science. Part IV: Canonical forms for equations involving higher order gradients
- A unifying perspective on linear continuum equations prevalent in physics. Part V: resolvents; bounds on their spectrum; and their Stieltjes integral representations when the operator is not selfadjoint