Uniqueness of the Solution of the Cauchy Problem for Parabolic Systems

Baderko, E. A.; Черепова, М. Ф.

doi:10.1134/s0012266119060077

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2021

2023

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Cited by 6 publications

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“…At that, there were considered the systems with both fixed and variable coefficients having different properties. Comprehensive results were obtained on the structure and properties of solutions, as well as on the correct solvability of boundary value problems, in particular, the Cauchy problem, in different functional spaces [3][4][5][6][7][8][9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Peculiarities of the Fundamental Solution of Parabolic Systems with a Negative Genus

Litovchenko¹

2021

Recent Developments in the Solution of Nonlinear Differential Equations

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For the parabolic Shilov-type systems with a negative genus, a method of studying the properties of a fundamental solution of the Cauchy problem is proposed. This method allows to improve the known estimates of Zhitomirskii fundamental solution for systems with dissipative parabolicity and describe the features of this solution more accurately. It opens wide possibilities for constructing a classical theory of the Cauchy problem for parabolic systems with negative genus and variable coefficients.

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