| Abstrakt: |
We show existence and uniqueness of global strong solutions for any initial data $${u_0 \in H^s(\mathbb{R}^d)}$$ , with $${d\in \{1,2\}, s \geq 3}$$ , of the general equation of surface growth models arising in the context of epitaxy thin films in the presence of the coarsening process, density variations and the Ehrlich-Schwoebel effect. Up to now, the problem of existence and smoothness of global solutions of such equations remains open in $${\mathbb{R}^d, d \in \{1,2\}}$$ . In this article, we show that taking into account of the main physical phenomena and a better approximation of terms related to them in the mathematical model lead to a kind of 'cancelation' of nonlinear terms between them in some spaces, and from this, we obtain existence and uniqueness of global strong solutions for such equations in $${\mathbb{R}^d, d \in \{1,2\}}$$ . [ABSTRACT FROM AUTHOR] |
Full text from SpringerLink