On the existence and asymptotic behavior of solutions for some swelling-porous problems

Our focus in this project is on the existence and the asymptotic behavior of solutions for some swelling-porous problems. We note that the swelling (also called expansive) soils have been characterized under porous media theory. In fact, swelling soils contain clay minerals that attract and absorb water, which leads to increase in pressure. This is considered to be sources of problems and harms in architectural and civil engineering. Swelling soils cause serious engineering problems such as uneven foundation settlement especially when it exceeds 10 % in most of expansive clay. The uneven foundation settlement could lead to minor or major cracking in the building structure or cause an undulation in road pavements. The evidence available has shown that expansive soils spread across all continents and estimates indicate that about 20-25% of land area in the United State is covered with such problematic soils with the accompanied economic loss of 5.5 to 7 billion USD in 2003 [32]. Hence, it is crucial to study the ways to annihilate or at least minimize such damages. Precisely in this project, we consider several problems related to swelling porous media and look for appropriate conditions to obtain solutions. We also discuss the long-time behavior of the solutions when they exist