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The article aims to map the Liberec region from the perspective of visitors with special needs and provide recommendations for the future development of accessible tourism in the region. The article explores the requirements of individuals with medical disabilities, as well as other groups such as mothers with strollers, pregnant women, the elderly, and people with dietary restrictions. This approach offers a comprehensive solution to a gap in academic literature, which often concentrates solely on individuals with disabilities. The study examines the relationship between age and disabilities of respondents, their participation in travel, and the difficulties encountered when choosing destinations in the region. To analyze correlations and frequencies related to age, disabilities, and travel participation, the study formulated three research questions and corresponding hypotheses and employed statistical tests. Descriptive statistics, chi-square tests, and frequency tables were used to analyze the data. Data collection involved primary and secondary sources, including professional literature, tourism reports, and specialized portals. Primary data was gathered through a questionnaire survey and semi-structured interviews. The survey targeted diverse groups with specific needs, focusing on the region's accessibility for barrier-free tourism. The study's comprehensive scope and unique regional focus provide valuable insights into enhancing accessible tourism in the Liberec region. The study highlights the cultural and natural attractions of the region. It suggests improving accessibility-related aspects such as accommodations, gastronomy facilities, transport, and information centres. Tailoring services, increasing destination awareness, improving infrastructure, and promoting inclusivity are recommended. The aim is for the Liberec region to become an inclusive tourist destination, achieved through physical improvements and promoting societal changes that embrace diversity and accessibility.

We consider boundary value problems for a nonlinear mass transfer model, which generalizes the classical Boussinesq approximation, under inhomogeneous Dirichlet boundary conditions for the velocity and the substance’s concentration. It is assumed that the leading coefficients of viscosity and diffusion and the buoyancy force in the model equations depend on concentration. We develop a mathematical apparatus for studying the inhomogeneous boundary value problems under consideration. It is based on using a weak solution of the boundary value problem and on the construction of liftings of the inhomogeneous boundary data. They remove the inhomogeneity of the data and reduce initial problems to equivalent homogeneous boundary value problems. Based on this apparatus we will prove the theorem of the global existence of a weak solution to the boundary value problem under study and establish important properties of the solution. In particular, we will prove the validity of the maximum principle for the substance’s concentration. We will also establish sufficient conditions for the problem data, ensuring the local uniqueness of weak solutions.