On problems for singular parabolic systems without initial conditions
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We consider a boundary-value problem without initial conditions for B -parabolic systems that contain even-order derivatives with respect to the space variable. For the problem under study, we obtain an integral representation of its solution via the Green function. In this representation, we take into account the restrictions by time imposed on the boundary functions and the inhomogeneity of the system. We also obtain a representation of the solution of a model boundary-value problem with the help of Poisson kernels and establish conditions for the existence of this solution.
KeywordsHeat Conduction Equation Parabolic System Poisson Kernel Liouville Theorem Bessel Operator
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