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.File allegati a questo prodotto
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