Abstract
We analyze the solvability of the inverse boundary problem with an unknown coefficient depended on time for the pseudo hyperbolic equation of fourth order with periodic and integral conditions.The initial problem is reduced to an equivalent problem. With the help of the Fourier method, the equivalent problem is reduced to a system of integral equations. The existence and uniqueness of the solution of the integral equations is proved. The obtained solution of the integral equations is also the only solution to the equivalent problem. Basing on the equivalence of the problems, the theorem of the existence and uniqueness of the classical solutions of the original problem is proved.
Highlights
There are many cases where the needs of the practice bring about the problems of determining coefficients or the right hand side of differential equations from some knowledge of its solutions
We analyze the solvability of the inverse boundary problem with an unknown coefficient depended on time for the pseudo hyperbolic equation of fourth order with periodic and integral conditions.The initial problem is reduced to an equivalent problem
With the help of the Fourier method, the equivalent problem is reduced to a system of integral equations
Summary
There are many cases where the needs of the practice bring about the problems of determining coefficients or the right hand side of differential equations from some knowledge of its solutions. Such problems are called inverse boundary value problems of mathematical physics. Different inverse problems for various types of partial differential equations have been studied in many papers. Due to the ( Mehraliyev, 2011)-( Mehraliyev, 2012), we proved the existence and uniqueness of the solution of the inverse boundary value problem for the pseudohyperbolic equation of fourth order with periodic and integral conditions.
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