Goursat-Type Problem for a Higher-Order Equation
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For a higher-order equation with leading mixed derivative, we consider the Goursat-type problem without consistency conditions. The notion of fundamental solution is introduced. By using this notion, we obtain a representation of the solution of the analyzed problem.
KeywordsIntegral Representation Fundamental Solution Consistency Condition Adjoint Operator Adjoint Equation
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- 1.A. N. Tikhonov and A. A. Samarskii, Equations of Mathematical Physics [in Russian], Nauka, Moscow (1977).Google Scholar
- 2.A. M. Nakhushev, Equations of Mathematical Biology [in Russian], Vysshaya Shkola, Moscow (1995).Google Scholar
- 4.M. B. Vinogradov, O. V. Rudenko, and A. P. Sukhorukov, Theory of Waves [in Russian], Nauka Moscow (1979).Google Scholar
- 8.V. I. Zhegalov and E. A. Utkina, “On one pseudoparabolic equation of the third order,” Izv. Vyssh. Uchebn. Zaved., Ser. Mat., 10, 73–76 (1999).Google Scholar
- 9.S. M. Nikol’skii, “On stable boundary values of a differentiable function of many variables,” Mat. Sb., (63)103, No. 2, 224–252 (1963).Google Scholar