On the well-posed solvability of the Dirichlet problem for a generalized mangeron equation with nonsmooth coefficients
For a fourth-order pseudoparabolic equation with nonsmooth coefficients, we consider the Dirichlet problem with nonclassical conditions that do not require matching conditions. We justify the equivalence of these conditions to classical boundary conditions for the case in which the solution of the problem is sought in an isotropic Sobolev space. The problem is solved by reduction to a system of Fredholm equations whose well-posed solvability is proved under nonsmooth conditions on the coefficients of the equation by the integral representation method.
KeywordsDirichlet Problem Operator Versus Fredholm Equation Aller Equation Classical Boundary Condition
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