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Purpose: The article aims to emphasize the importance of a multifaceted and detailed analysis of the problem of protection and using modes of immovable cultural heritage, considering the heritage types and involving investors in this process. Design/Methodology/Approach: The monographic method was used for the scientific literature and legal provisions (especially Lithuanian law) analysis. Additionally, the websites, of the presented dilemmas of the buyers of immovable monuments, were analyzed. Findings: Research results confirm that the immovable cultural heritage has a complex nature, and decisions about their usage modes, should be investigated deeper. One should strive to maintain their uniqueness, but also to implement a system that reduces the risk of investors who decide to invest in the revalorization of historic buildings. Practical Implications: The article will make the current owner (State, local community) and potential investors more aware of the factors that should be considered when managing their or deciding to purchase a property constituting cultural heritage. Originality/Value: Authors proposed the model of the risk identification and restrictions connected with the purchase and management of property constituting cultural heritage by potential investors.

This work presents a proof of convergence of a discrete solution to a continuous one. At first, the continuous problem is stated as a system of equations which describe the filtration process in the pressing section of a paper machine. Two flow regimes appear in the modeling of this problem. The model for the saturated flow is presented by the Darcy’s law and the mass conservation. The second regime is described by the Richards’ approach together with a dynamic capillary pressure model. The finite volume method is used to approximate the system of PDEs. Then, the existence of a discrete solution to the proposed finite difference scheme is proven. Compactness of the set of all discrete solutions for different mesh sizes is proven. The main theorem shows that the discrete solution converges to the solution of the continuous problem. At the end we present numerical studies for the rate of convergence.