<p>This work is devoted to the study of the solvability of boundary value problems for a parabolic equation with involution using the potential theory method. A nonlocal parabolic equation is introduced using involutive transformations with respect to the spatial variable. Using the fundamental solution, heat potentials are introduced, and their properties are studied. Using these properties and methods from the theory of integral equations, the second boundary value problem for a parabolic equation with involution was solved. The solution to this problem is constructed in explicit form, and the uniqueness of the solution is proven using the method of apriori estimates.</p>

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THE METHOD OF POTENTIALS FOR THE HEAT EQUATION WITH INVOLUTION

  • Dilfuza E. Uzaqbaeva

摘要

This work is devoted to the study of the solvability of boundary value problems for a parabolic equation with involution using the potential theory method. A nonlocal parabolic equation is introduced using involutive transformations with respect to the spatial variable. Using the fundamental solution, heat potentials are introduced, and their properties are studied. Using these properties and methods from the theory of integral equations, the second boundary value problem for a parabolic equation with involution was solved. The solution to this problem is constructed in explicit form, and the uniqueness of the solution is proven using the method of apriori estimates.