We improve in two ways the well-posedness results of \cite{AS2} for a slow erosion model proposed in \cite{HK}: firstly we study the asymptotic profile when $\frac{u_0}{1+u_0}\in L^\infty$, where $u_0$ is the initial datum; moreover, using a compensated compactness based argument we prove the existence of solutions when $\frac{u_0}{1+u_0}\in L^\sigma$, $\sigma\ge3.$
Well-Posedness for a Slow Erosion Model / Coclite, Giuseppe Maria; Jannelli, E.. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - 456:1(2017), pp. 337-355. [10.1016/j.jmaa.2017.07.006]
Well-Posedness for a Slow Erosion Model
COCLITE, Giuseppe Maria;
2017-01-01
Abstract
We improve in two ways the well-posedness results of \cite{AS2} for a slow erosion model proposed in \cite{HK}: firstly we study the asymptotic profile when $\frac{u_0}{1+u_0}\in L^\infty$, where $u_0$ is the initial datum; moreover, using a compensated compactness based argument we prove the existence of solutions when $\frac{u_0}{1+u_0}\in L^\sigma$, $\sigma\ge3.$File in questo prodotto:
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