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Mixed problem for a third order parabolic-hyperbolic model equation

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The study demonstrates the formulation of a boundary value problem for a third-order parabolic-hyperbolic equation in a mixed domain.
Existence and uniqueness theorems for a regular solution are proved, utilizing energy integrals and integral equations.
A degenerate hyperbolic equation of the second order and a nonhomogeneous third-order equation are analyzed within the mixed domain.
Sufficient smoothness conditions are identified to ensure the regularity of the obtained solution.

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This research formulates a boundary value problem for third-order parabolic-hyperbolic equations, highlighting existence and uniqueness theorems.

Zhiraslan Anatolievich Balkizov (2025) studied this question.

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This research formulates a boundary value problem for third-order parabolic-hyperbolic equations, highlighting existence and uniqueness theorems.