×

Solution of a problem of heat conduction theory with a discontinuous coefficient and degenerate moving boundaries. (Russian) Zbl 0557.35066

A heat conduction problem is considered for the equation \(\partial u/\partial t=a^ 2(x)\partial^ 2u/\partial x^ 2\) in the region \([D_ 1(-\alpha_ 1t<x<0)\cup D_ 2(0<x<\alpha_ 2t)]\times (T(t>0)),\) degenerating at \(t=0\), the boundaries of which are moving a linear manner and \(a^ 2(x)=a^ 2_ 1\quad for\quad -\alpha_ 1t<x<0,\quad a^ 2(x)=a^ 2_ 2\quad for\quad 0<x<\alpha_ 2t,\) with boundary conditions \(u(\bar +\alpha_{1,2}t,\quad t)=g_{1,2}(t)\) and ideal thermal contact conditions at \(x=0\) \((t>0)\). The problem is reduced to an integral equation of a special form the resolvent kernel of which can be found from some recurrent relationships.
Reviewer: I.Zino

MSC:

35K20 Initial-boundary value problems for second-order parabolic equations
35R05 PDEs with low regular coefficients and/or low regular data
80A20 Heat and mass transfer, heat flow (MSC2010)
74A15 Thermodynamics in solid mechanics
PDFBibTeX XMLCite