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Strong maximum principles for parabolic nonlinear problems with nonlocal inequalities together with integrals

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  • Ludwik Byszewski

Abstract

In [4] and [5], the author studied strong maximum principles for nonlinear parabolic problems with initial and nonlocal inequalities, respectively. Our purpose here is to extend results in [4] and [5] to strong maximum principles for nonlinear parabolic problems with nonlocal inequalities together with integrals. The results obtained in this paper can be applied in the theories of diffusion and heat conduction, since considered here integrals in nonlocal inequalities can be interpreted as mean amounts of the diffused substance or mean temperatures of the investigated medium.

Suggested Citation

  • Ludwik Byszewski, 1990. "Strong maximum principles for parabolic nonlinear problems with nonlocal inequalities together with integrals," International Journal of Stochastic Analysis, Hindawi, vol. 3, pages 1-15, January.
    • Handle: RePEc:hin:jnijsa:394325
    DOI: 10.1155/S1048953390000065
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