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On Some Global Existence Theorems for a Semilinear Parabolic Problem

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Applied Nonlinear Analysis

Abstract

Some conditions are obtained sufficient for solutions to a non-linear parabolic equation of second order with non-linear boundary conditions to be bounded or to tend to infinity at a finite time.

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References

  1. Fujita, H. (1996). On the blowing up of the solutions for ut=Δu+u1+α. J. Fac. Sci. Univ. Tokyo, Sect. I, 13:109–124.

    Google Scholar 

  2. Fujita, H. (1970) On some nonexistence and nonuniqueness theorems for nonlinear parabolic equations. Proc. of Symposia in Pure Mathematics, XVIII,4:105–113.

    Google Scholar 

  3. Levine, H.A. and Payne, L.E. (1974). Some nonexistence theorems for initial-boundary value problems with nonlinear boundary constraints. Proc. of AMS, 46,7:277–284.

    MathSciNet  Google Scholar 

  4. Walter, W. (1975). On existence and nonexistence in the large of solutions of parabolic differential equations with a nonlinear boundary condition. SIAM J. Math. Anal., 6:5–90.

    Article  Google Scholar 

  5. Esher, J. (1989). Global existence and non-existence of semilinear parabolic equations with nonlinear boundary conditions. Math. Ann., 284:285–305.

    MathSciNet  Google Scholar 

  6. Kamin, S., Peletier, L.A. and Vazquez, J.L. (1989). Classification of singular solutions of a nonlinear heat equation. Duke Math. J., 58:243–263.

    Article  MathSciNet  Google Scholar 

  7. Levine, H.A. (1990). The role of critical exponents in blowup theorems. SIAM Review, 32:262–288.

    Article  MathSciNet  MATH  Google Scholar 

  8. Gómez, J.L., Márquez, V. and Wolanski, N. (1991). Blow-up results and localization of blow-up points for the heat equation with a nonlinear boundary condition. J. Differential Equations, 92:384–401.

    MathSciNet  Google Scholar 

  9. Chipot, M., Fila, M. and Quittner, P. (1991). Stationary solutions, blow-up and convergence to stationary solutions for semilinear parabolic equations with nonlinear boundary conditions. Acta Math. Univ. Comenian., LX,1:35–103.

    MathSciNet  Google Scholar 

  10. Quittner, P. (1991). On global existence and stationary solutions for two classes of semilinear parabolic problems. Comment. Math. Univ. Carolin., 34:105–124.

    MathSciNet  Google Scholar 

  11. Egorov, Yu. V. and Kondratiev, V.A. (1996). On a nonlinear boundary problem for a heat equation. C. R. Acad. Sci. Paris, Série I, 322:55–58.

    MathSciNet  Google Scholar 

  12. Egorov, Yu. V. and Kondratiev, V.A. (1998). Two theorems on blow-up solutions for semilinear parabolic equations of second order C. R. Acad. Sci. Paris, Série I, 327:47–52.

    MathSciNet  Google Scholar 

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© 2002 Kluwer Academic Publishers

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Egorov, Y.V., Kondratiev, V.A. (2002). On Some Global Existence Theorems for a Semilinear Parabolic Problem. In: Sequeira, A., da Veiga, H.B., Videman, J.H. (eds) Applied Nonlinear Analysis. Springer, Boston, MA. https://doi.org/10.1007/0-306-47096-9_6

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  • DOI: https://doi.org/10.1007/0-306-47096-9_6

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-0-306-46303-7

  • Online ISBN: 978-0-306-47096-7

  • eBook Packages: Springer Book Archive

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