On strongly loaded heat equations

Abstract

The article is devoted to the research of boundary value problems for the spectrum - loaded operator of heat conduction with the moving point of loading to the temporary axle in zero or on infinity. For strongly loaded parabolic 2k-order equations the adjoint boundary value problems, when order of loaded term is greater then one of differential part of equation, is studied. In this article we continue a investigation of the boundary value problems for spectrally loaded parabolic equations in unbounded domains.The boundary value problem for the spectral-loaded equation of thermal conductivity, which on the one hand is quite close to the problems with the load containing the second derivative of the spatial variable, and is of independent interest on the other hand in this work, is considered.