5 problems

Consider the multiscale elliptic equation referenced as, with forcing term $f=0$, and let $(\varepsilon_i)_{1\le i\le n}$ be the oscillation scales, without imposing any scale-sepa…

Backward-theory homogenization conjecture. A backward-theory approach to the slowly varying theory should support a cognate generalized homogeneous wave equation

Higher-order truncation conjecture. Truncations to orders other than quadratic should give corresponding analysis and results.

Multiscale hierarchy conjecture. Dynamical models on simplicial complexes can display a multiscale hierarchy, where higher-order simplices equilibrate before lower-order simplices…

A nonlinear dispersive $\mathbb{Z}^2$-lattice equation is considered together with its lowest-order multiscale reduction, obtained through the multiscale expansion formalism. The r…