Some direct and inverse problems of mathematical physics
Stationary and non-stationary diffusion
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The problems of nonlocal type have been repeatedly studied earlier. The main principal property of these problems is their non-selfadjointness. It causes the main difficulties in their analytical and numerical solutions. Assuming strong singularity of boundary conditions of the problem, the well-posedness of its formulation can be proved by Fourier method of separation of variables. The problems, boundary conditions of which do not have the property of strong regularity are less studied. We have considered the question of existence of the regular and strong solution of a differential problem, ...
The problems of nonlocal type have been repeatedly studied earlier. The main principal property of these problems is their non-selfadjointness. It causes the main difficulties in their analytical and numerical solutions. Assuming strong singularity of boundary conditions of the problem, the well-posedness of its formulation can be proved by Fourier method of separation of variables. The problems, boundary conditions of which do not have the property of strong regularity are less studied. We have considered the question of existence of the regular and strong solution of a differential problem, its uniqueness and stability of initial data in various metrics. The monograph also deals with inverse problems. The monograph is intended for specialists in the field of differential equations and the theory of differential operators, doctoral students, as well as for undergraduates and senior students specializing in this field. And also can be used for drawing up of special courses on differential equations in higher educational institutions.
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