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The problem domain is the area of the real-world system that the application will deal with. It describes the context in which the software solution will operate and the entities and relationships that exist within that context. Problem domain description is crucial because it helps the development team to understand the requirements and build a useful and effective application.

In a software development team, there are different roles and responsibilities assigned to individuals for effective project management and implementation. Some key roles include project manager, business analyst, software architect, developer, and quality assurance personnel. The specific roles and responsibilities can vary depending on the organization and the specific project.

The responsibility of writing the problem domain description typically falls on the business analyst (BA). The business analyst is the person who liaises between the stakeholders (clients or end-users) and the development team. They gather and analyze the requirements, create comprehensive and clear documentation both for understanding the problem domain and for further use during development. The BA's main objective is to ensure that the correct problem is being addressed and that the software solution will meet the clients' or end-users' needs. However, it's essential to note that the entire development team should have a clear understanding of the problem domain and work closely with the business analyst to ensure that the application being developed effectively addresses the problem domain.