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Increasing solutions of linear second-order equations with nonnegative characteristic form

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Abstract

In a layer H{0< t ≤ T, x ε Rn we consider a linear second-order parabolic equation that degenerates on an arbitrary subset ¯H. It is assumed that the coefficient of the time derivative has a zero of sufficiently high order on the hyperplane t=0; as a consequence, the Cauchy problem will be unsolvable. The exact bounds are obtained of the permissible growth of the sought-for function when ¦x¦→ ∞, ensuring a single-valued solution of the problem without initial data.

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Authors and Affiliations

  1. M. V. Lomonosov Moscow State University, USSR

    A. S. Kalashnikov

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  1. A. S. Kalashnikov
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Translated from Matematicheskie Zametki, Vol. 3, No. 2, pp. 171–178, February, 1968.

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Kalashnikov, A.S. Increasing solutions of linear second-order equations with nonnegative characteristic form. Mathematical Notes of the Academy of Sciences of the USSR 3, 110–114 (1968). https://doi.org/10.1007/BF01094330

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  • DOI: https://doi.org/10.1007/BF01094330

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