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<p>In this paper we study the influence of an absorption term of power type on the regularity and time behavior of the solutions to a class of nonlinear parabolic problems. We will show that important and unexpected changes occur. For example, in absence of a forcing term it can produce an immediate boundedness in cases when it is well known that, in absence of such a lower-order term, the solutions remain unbounded. Moreover, we prove that regularization phenomena appear also in presence of forcing terms.</p>

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On the influence of some absorption terms on the solutions of nonlinear parabolic equations

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  • 发表日期：

    2025年5月2日

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  • Maria Michaela Porzio

摘要

In this paper we study the influence of an absorption term of power type on the regularity and time behavior of the solutions to a class of nonlinear parabolic problems. We will show that important and unexpected changes occur. For example, in absence of a forcing term it can produce an immediate boundedness in cases when it is well known that, in absence of such a lower-order term, the solutions remain unbounded. Moreover, we prove that regularization phenomena appear also in presence of forcing terms.