In this paper we investigate a mixed parabolic-hyperbolic initial boundary value problem in two disconnected intervals with Robin-Dirichlet conjugation conditions. A finite difference scheme approximating this problem is proposed and analyzed. An estimate of the convergence rate is obtained.

This paper deals with an application of complex analysis to second order equations of mixed type. We mainly discuss the discontinuous Poincaré boundary value problem for a second order linear equation of mixed (elliptic-hyperbolic) type, i.e. the generalized Lavrent’ev-Bitsadze equation with weak conditions, using the methods of complex analysis. We first give a representation of solutions for the above boundary value problem, and then give solvability conditions via the Fredholm theorem for integral...

We study the asymptotic behaviour of a sequence of strongly degenerate parabolic equations ${\partial }_t\left(r_{h}u\right)-\mathrm{div}(a_h·Du)$ with $r_h(x,t)\ge 0$, $r_h\in L^{\infty }(\Omega \times (0,T))$. The main problem is the lack of compactness, by-passed via a regularity result. As particular cases, we obtain G-convergence for elliptic operators $(r_h\equiv 0)$, G-convergence for parabolic operators $(r_h\equiv 1)$, singular perturbations of an elliptic operator $(a_h\equiv a$ and $r_h\to r$, possibly $r\equiv 0)$.