On a periodic solution of the parabolic singularly perturbed equation with different powers of a small parameter multiplying the first and second derivatives (Q5954755)

The authors consider a singularly perturbed parabolic equation with a small parameter \({\varepsilon}^2\) multiplying the second derivative of the solution \(u(x,t,\varepsilon)\) with respect to \(x\) and with a small parameter \(\varepsilon\) multiplying the first derivative with respect to \(t\). The existence of a periodic steplike solution is proved and the limit properties of this solution as \({\varepsilon}\rightarrow 0\) are established.