### Journals Information

**
Mathematics and Statistics Vol. 10(3), pp. 498 - 514 DOI: 10.13189/ms.2022.100305 Reprint (PDF) (383Kb) **

## Half-Space Model Problem for Navier-Lamé Equations with Surface Tension

**Sri Maryani ^{1}^{,*}, Bambang H Guswanto ^{1}, Hendra Gunawan ^{2}**

^{1}Department of Mathematics, Jenderal Soedirman University, Indonesia

^{2}Department of Mathematics, Bandung Institute of Technology, Indonesia

**ABSTRACT**

Recently, we have seen the phenomena in use of partial differential equations (PDEs) especially in fluid dynamic area. The classical approach of the analysis of PDEs were dominated in early nineteenth century. As we know that for PDEs the fundamental theoretical question is whether the model problem consists of equation and its associated side condition is well-posed. There are many ways to investigate that the model problems are well-posed. Because of that reason, in this paper we consider the -boundedness of the solution operator families for Navier-Lamé equation by taking into account the surface tension in a bounded domain of -dimensional Euclidean space (≥ 2) as one way to study the well-posedess. We investigate the -boundedness in half-space domain case. The -boundedness implies not only the generation of analytic semigroup but also the maximal regularity for the initial boundary value problem by using Weis's operator valued Fourier multiplier theorem for time dependent problem. It was known that the maximal regularity class is the powerful tool to prove the well-posesness of the model problem. This result can be used for further research for example to analyze the boundedness of the solution operators of the model problem in bent-half space or general domain case.

**KEYWORDS**

-sectoriality, Navier-Lamé equation, Surface Tension, Half-space

**Cite This Paper in IEEE or APA Citation Styles**

(a). IEEE Format:

[1] Sri Maryani , Bambang H Guswanto , Hendra Gunawan , "Half-Space Model Problem for Navier-Lamé Equations with Surface Tension," Mathematics and Statistics, Vol. 10, No. 3, pp. 498 - 514, 2022. DOI: 10.13189/ms.2022.100305.

(b). APA Format:

Sri Maryani , Bambang H Guswanto , Hendra Gunawan (2022). Half-Space Model Problem for Navier-Lamé Equations with Surface Tension. Mathematics and Statistics, 10(3), 498 - 514. DOI: 10.13189/ms.2022.100305.