We study a parabolic equation with the data and the coefficient of zero order term only summable functions. Despite all this lack of regularity we prove that there exists a solution which becomes immediately bounded. Moreover, we study the asymptotic behavior of this solution in the autonomous case showing that the constructed solution tends to the associate stationary solution.

Existence and asymptotic behavior of a parabolic equation with L1 data / Moreno, Lourdes; Porzio, Maria Michaela. - In: ASYMPTOTIC ANALYSIS. - ISSN 0921-7134. - 118:(2020), pp. 148-159. [10.3233/ASY-191558]

Existence and asymptotic behavior of a parabolic equation with L1 data

Maria Michaela Porzio
2020

Abstract

We study a parabolic equation with the data and the coefficient of zero order term only summable functions. Despite all this lack of regularity we prove that there exists a solution which becomes immediately bounded. Moreover, we study the asymptotic behavior of this solution in the autonomous case showing that the constructed solution tends to the associate stationary solution.
regularizing effect; asymptotic behavior; regularity of solutions; linear parabolic equations
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Existence and asymptotic behavior of a parabolic equation with L1 data / Moreno, Lourdes; Porzio, Maria Michaela. - In: ASYMPTOTIC ANALYSIS. - ISSN 0921-7134. - 118:(2020), pp. 148-159. [10.3233/ASY-191558]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1305562
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