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On positive solutions of the heat equation satisfying a nonlinear boundary condition

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Abstract

We consider a boundary value problem for the heat equation in the exterior of a bounded domain of space variables. On the boundary of the domain, we pose a nonlinear boundary condition. We find sharp nonlinearity exponents for which there exists no global solution.

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References

  1. Fujita, On the Blowing up of Solutions of the Cauchy Problem u t = Δu + u 1+α, J. Fac. Sci. Univ. Tokyo. Sect. 1 A. Math., 1966, vol. 13, pp. 105–113.

    Google Scholar 

  2. Haykawa, On the Nonexistence of Global Solutions of Some Semilinear Parabolic Equations, Proc. Japan. Acad., 1973, vol. 49, pp. 503–505.

    Article  MathSciNet  Google Scholar 

  3. Fila, M. and Quittner, P., The Blow-Up for the Heat Equation with a Nonlinear Boundary Conditions, Math. Methods Appl. Sci., 1991, vol. 14, pp. 197–205.

    Article  MATH  MathSciNet  Google Scholar 

  4. Galaktionov, V.A. and Levine, H.A., On Critical Fujita Exponents for Heat Equations with Nonlinear Flux Conditions on the Boundary, Israel J. Math., 1996, vol. 94, pp. 125–146.

    Article  MATH  MathSciNet  Google Scholar 

  5. Hu, B. and Yin, H.-M., On Critical Exponents for the Heat Equation with a Nonlinear Boundary Condition, Ann. Inst. H. Poincaré, 1996, vol. 13, pp. 707–732.

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    V. A. Kondrat’ev

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  1. V. A. Kondrat’ev
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Original Russian Text © V.A. Kondrat’ev, 2010, published in Differentsial’nye Uravneniya, 2010, Vol. 46, No. 8, pp. 1104–1112.

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Kondrat’ev, V.A. On positive solutions of the heat equation satisfying a nonlinear boundary condition. Diff Equat 46, 1114–1122 (2010). https://doi.org/10.1134/S0012266110080057

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  • DOI: https://doi.org/10.1134/S0012266110080057

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