Abstract
Abstract We consider boundary value problems for biquaternion wave (biwave) equations. Such equations are biquaternion generalizations of the Maxwell and Dirac equations. Monochromatic solutions with a fixed oscillation frequency are studied. Fundamental and generalized solutions are constructed for biquaternion oscillation amplitudes in the space of generalized biquaternions whose components are tempered distributions. Using the method of distributions, we find solutions of the biwave equation in a bounded domain for known solution values on the boundary and give regular integral representations of the solutions at interior points and an integral representation of the characteristic function of the domain in terms of the fundamental solution of the equation. On the basis of the last of these formulas, which is a biquaternion analog of the well-known Green and Gauss formulas for elliptic equations, we construct resolving singular boundary integral equations for stationary boundary value problems.