Article

Some non‐local problems for the parabolic‐hyperbolic type equation with complex spectral parameter

Erkinjon KarimovInstitute of Mathematics and Information Technologies, Uzbek Academy of Sciences, F. Khodjaev st. 29, Tashkent-125, Uzbekistan

Mathematische Nachrichtenjournal2008en

ABI

Abstract

Abstract In the present paper the unique solvability of two non‐local problems for the mixed parabolic‐hyperbolic type equation with complex spectral parameter is proved. Sectors for values of the spectral parameter where these problems have unique solutions are shown. Uniqueness of the solution is proved by the method of energy integral and existence is proved by the method of integral equations. In particular cases, eigenvalues and corresponding eigenfunctions of the studied problems are found. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Topics

Differential Equations and Boundary Problems Differential Equations and Numerical Methods Stability and Controllability of Differential Equations

Identifiers

DOI: 10.1002/mana.200510652

Citations and references

Cited by 6 4 references

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