On the Dirichlet Problem in a Characteristic Rectangle for Fourth Order Linear Singular Hyperbolic Equations

Abstract

In the rectangle D = (0, $$\frac{{\partial ^4 u}}{{\partial x^2 \partial y^2 }} = p(x,y)u + q(x,y)$$ , $$u(x,y) = 0{\text{ for (}}x,y) \in \Gamma$$ is considered, where p and \(q:D \to \mathbb{R}\) are locally summable functions and may have nonintegrable singularities on Γ. The effective conditions guaranteeing the unique solvability of this problem and the stability of its solution with respect to small perturbations of the coefficients of the equation under consideration are established.