Classical solvability of the Cauchy problem for parabolic equations (Q2760611)
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scientific article; zbMATH DE number 1682180
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Classical solvability of the Cauchy problem for parabolic equations |
scientific article; zbMATH DE number 1682180 |
Statements
13 December 2001
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Tikhonov class of functions
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Zygmund conditions
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continuity modulus of a function
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isomoprhism property
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Classical solvability of the Cauchy problem for parabolic equations (English)
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General linear parabolic differential equations of the second order with variable coefficients are under study. Spaces of functions with qualified moduli of continuity are introduced, and it is shown that the problem under study has a classical solution provided both coefficients and right-hand sides of the equation belong to these spaces. Some necessary and sufficient conditions are found on moduli of continuity for the operator of the Cauchy problem to be an isomorphism between the corresponding spaces of solutions and right-hand sides.
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