Conjugate Problem for a Third Order Equation with Multiple Characteristics and a Positive Function at the Higher Order Derivative
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We establish the existence and uniqueness of a regular solution to the conjugate (generalized diffraction) problem for the equation ut − h(x)u xxx + c(x, t)u = f(x, t), where h(x) is positive and can have discontinuity of the first kind at the point x = 0.
KeywordsRegular Solution Regularization Method Multiple Characteristic Boundary Integral High Order Derivative
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- 1.T. D. Dzhuraev, Boundary Value Problems for Equations of Mixed and Mixed-Compound Type [in Russian], FAN, Tashkent (1986).Google Scholar
- 3.A. M. Abdrakhmanov and A. I. Kozhanov, “A problem with a nonlocal boundary condition for one class of odd-order equations” [in Russian], Izv. Vyssh. Uchebn. Zaved., Mat. No. 5, 3–12 (2007); English transl.: Russ. Math. 51, No. 5, 1–10 (2007).Google Scholar
- 5.V. I. Antipin, “Solvability of a boundary value problem for operator-differential equations of mixed type” [in Russian], Sib. Mat. Zh. 54, No. 2, 245–257 (2013); English transl.: Sib. Math. J. 54, No. 2, 185–195 (2013).Google Scholar