INITIAL-BOUNDARY VALUE PROBLEM FOR THE SECOND-ORDER MIXED TYPE DIFFERENTIAL EQUATION WITH ONE LINE OF DEGENERACY
Keywords:
mixed type equation, ill-posed problem, a priori estimate, set of correctness, regularization, quasi-inversionAbstract
In this paper, we study the initial-boundary-value problem for the inhomogeneous mixed type equation with one line of degeneration. An a priori estimate of solution is obtained with the help of energy integrals. The uniqueness theorem is proved and the conditional stability estimate is obtained. Approximate solutions of the problem are constructed by regularization and quasi-inversion methods.
References
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