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

Authors:

Affiliation:

(1) Faculty of Physics, Chair of Higher Mathematics, I. Javakhishvili Tbilisi State University, 3, Chavchavadze Ave., Tbilisi, 380028, Georgia

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 Gamma

. 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.

Keywords:

Fourth order linear singular hyperbolic equation Dirichlet problem existence uniqueness and stability of a solution

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