ON THE UNIQUENESS OF THE SOLUTION OF A NONLINEAR BOUNDARY VALUE PROBLEM FOR A THIRD-ORDER EQUATION WITH MULTIPLE CHARACTERISTICS ON A PLANE
Keywords:
a nonlinear boundary value problem, a solution, a uniqueness, the energy integral method.Abstract
In this paper, we study a nonlinear boundary value problem for a third-order partial differential equation with multiple characteristics defined on a plane domain. Equations of this type arise in various problems of mathematical physics and often present significant analytical difficulties due to the presence of nonlinear terms associated with multiple characteristic directions. We formulate an appropriate boundary value problem and analyze the conditions under which the problem admits a solution in the class of continuous functions. Particular attention is devoted to the influence of the nonlinear structure and the characteristic properties of the differential operator on the solvability of the problem. The main result of the paper establishes the uniqueness of a solution in the specified functional class. The proof is based on the construction of suitable energy integrals and the application of the energy integral method. The obtained results contribute to the theory of nonlinear boundary value problems for higher-order partial differential equations with multiple characteristics. They may be useful in the further study of similar classes of nonlinear equations.
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CMFD, 2025, Volume 71, Issue 1, 18–32
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