BOUNDARY-VALUE PROBLEMS WITH IMPULSIVE CONDITIONS FOR PARABOLIC EQUATIONS WITH DEGENERATIONS

摘要

We consider the first boundary-value problem and the unilateral boundary-value problem with impulsive conditions with respect to the time variable for a linear parabolic equation with power singularities of any order in the space variables. With the help of the maximum principle and a priori estimates, we establish the existence and uniqueness of the solutions of the posed problems in the Holder spaces with power weights.