Abstract
Linear parabolic equations with coefficients of the lower-order terms unbounded, and with a small parameter multiplying some of the second (highest) space derivatives are considered, in the limiting case when such a parameter goes to zero. This yields a degenerate parabolic (ultraparabolic) equation with one space-like variable, $x$, and two time-like variables, $y$ and $t$. No boundary-layer is found to be needed in the case of the boundary-value problem on the $x$-unbounded domain $\mathcal{Q}_T=\{(x,y,t)\in \mathbb{R}\times [0,1]\times[0,T]\}$ with a periodic boundary condition in the variable $y$ and initial data at $t=0$.
Citation
Denis R. Akhmetov. Mikhail M. Lavrentiev Jr.. Renato Spigler. "Singular perturbations for parabolic equations with unbounded coefficients leading to ultraparabolic equations." Differential Integral Equations 17 (1-2) 99 - 118, 2004. https://doi.org/10.57262/die/1356060474
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