In this paper we study a class of nonlinear parabolic problems including the p-Laplacian equation. The initial datum and the forcing term are allowed to be summable functions or Radon measures. We prove that these equations have surprising regularizing properties. Moreover, we study the behavior in time of these solutions proving that decay estimates hold true also for non zero reaction terms. Finally, we study the autonomous case.

Asymptotic behavior and regularity properties of strongly nonlinear parabolic equations / PORZIO, Maria Michaela. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - (2019). [10.1007/s10231-019-00845-w]

Asymptotic behavior and regularity properties of strongly nonlinear parabolic equations

Maria Michaela Porzio
2019

Abstract

In this paper we study a class of nonlinear parabolic problems including the p-Laplacian equation. The initial datum and the forcing term are allowed to be summable functions or Radon measures. We prove that these equations have surprising regularizing properties. Moreover, we study the behavior in time of these solutions proving that decay estimates hold true also for non zero reaction terms. Finally, we study the autonomous case.
decay estimates, asymptotic behavior, regularity of solutions, p-Laplacian equation, nonlinear degenerate parabolic equations, smoothing effect
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Asymptotic behavior and regularity properties of strongly nonlinear parabolic equations / PORZIO, Maria Michaela. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - (2019). [10.1007/s10231-019-00845-w]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1305560
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