Generalized Solutions of Stationary Boundary Value Problems for Biwave Equations
Alexeyeva L.A.
April 2022Pleiades journals
Differential Equations
2022#58Issue 4475 - 487 pp.
Abstract: We consider boundary value problems for biquaternion wave (biwave) equations. Such equations are biquaternion generalizationsof the Maxwell and Dirac equations. Monochromatic solutions with a fixed oscillation frequencyare studied. Fundamental and generalized solutions are constructed for biquaternion oscillationamplitudes in the space of generalized biquaternions whose components are tempereddistributions. Using the method of distributions, we find solutions of the biwave equation in abounded domain for known solution values on the boundary and give regular integralrepresentations of the solutions at interior points and an integral representation of thecharacteristic function of the domain in terms of the fundamental solution of the equation. On thebasis of the last of these formulas, which is a biquaternion analog of the well-known Green andGauss formulas for elliptic equations, we construct resolving singular boundary integral equationsfor stationary boundary value problems.
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Institute of Mathematics and Mathematical Modeling, Ministry of Education andScienceof the Republic of Kazakhstan, Almaty, 050010, Kazakhstan
Institute of Mathematics and Mathematical Modeling
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