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Global Solvability of the Cauchy–Dirichlet Problem for the Class of Nondiagonal Parabolic Systems with q-Nonlinearity in the Gradient, 1 < q < 2

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Abstract

The Cauchy–Dirichlet problem for the class of nondiagonal q-nonlinear parabolic systems is studied, 1 < q < 2. In the case of two spatial variables, a solution that is global in time and smooth almost everywhere is constructed. Hausdorff's dimension of the singular set is estimated. Bibliography: 16 titles.

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  1. St.Petersburg State University, U.S.A

    A. A. Arkhipova

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  1. A. A. Arkhipova
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Arkhipova, A.A. Global Solvability of the Cauchy–Dirichlet Problem for the Class of Nondiagonal Parabolic Systems with q-Nonlinearity in the Gradient, 1 < q < 2. Journal of Mathematical Sciences 123, 4539–4564 (2004). https://doi.org/10.1023/B:JOTH.0000041473.41796.59

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  • DOI: https://doi.org/10.1023/B:JOTH.0000041473.41796.59

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