Existence and asymptotic behavior of a parabolic equation with L1 data

Article type: Research Article

Authors: Moreno-Mérida, Lourdes^a | Porzio, Maria Michaela^{b; *}

Affiliations: [a] Departamento de Analisis Matematico, Universidad de Granada, 18071 Granada, Spain. E-mail: lumore@ugr.es | [b] Dipartimento di Matematica, Sapienza Università di Roma, Piazzale A. Moro 2, 00185 Roma, Italy. E-mail: porzio@mat.uniroma1.it

Correspondence: [*] Corresponding author. E-mail: porzio@mat.uniroma1.it.

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.

Keywords: Regularizing effect, asymptotic behavior, regularity of solutions, linear parabolic equations

DOI: 10.3233/ASY-191558

Journal: Asymptotic Analysis, vol. 118, no. 3, pp. 143-159, 2020