UNIQUENESS OF THE SOLUTION OF A BOUNDARY VALUE PROBLEM FOR A NONCLASSICAL PARABOLIC-TYPE EQUATION
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Abstract
This paper investigates the uniqueness of the solution to a boundary value problem for a nonclassical parabolic-type differential equation. The problem is considered in a general form, and through appropriate substitutions the equation is simplified and formulated in a given domain with specified boundary conditions. The uniqueness of the solution is proved using the energy integral method, and it is shown that the corresponding homogeneous problem admits only the trivial solution. The obtained results are of significant importance in the theory of equations of mathematical physics and can be applied to the study of nonclassical boundary value problems.
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