A unifying perspective on linear continuum equations prevalent in science. Part I: Canonical forms for static, steady, and quasistatic equations
arXiv:2006.02215
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 I we elucidate the form for many static, steady, and quasistatic equations.
25 pages, no figures
References in corpus (5)
- Optical Hyperlens: Far-field imaging beyond the diffraction limit
- 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 VI: rapidly converging series expansions for their solution
- 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
Cited by in corpus (3)
- 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