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Parabolic equation with a singular potential

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Abstract

We study the existence of a nonnegative generalized solution of an initial-boundary value problem for the heat equation with a singular potential in an arbitrary bounded domain Ω ⊂ R n, n ≥ 3, containing the unit ball. We show that if the condition ∝ Ω V n/2+s|x|s dx ≤ c n is satisfied for some s ≥ 0 and c n = c n (n, s, Ω) > 0, then the problem in question has a nonnegative solution.

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References

  1. Baras, P. and Goldstein, J. A., The Heat Equation with a Singular Potential, Trans. Amer. Math. Soc., 1984, vol. 284, no. 1, pp. 121–139.

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Authors and Affiliations

  1. Turkmen Polytechnic University, Ashgabat, Turkmenistan

    B. A. Khudaigulyev

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  1. B. A. Khudaigulyev
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Original Russian Text © B.A. Khudaigulyev, 2009, published in Differentsial’nye Uravneniya, 2009, Vol. 45, No. 2, pp. 274–277.

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Khudaigulyev, B.A. Parabolic equation with a singular potential. Diff Equat 45, 282–285 (2009). https://doi.org/10.1134/S0012266109020189

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  • DOI: https://doi.org/10.1134/S0012266109020189

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