About this Research Topic

Background

Adequate mathematical modeling is the key to success for many real-world projects in engineering, medicine, and other applied areas. As soon as an appropriate mathematical model is developed, it can be comprehensively analyzed by a broad spectrum of available mathematical methods. For example, compartmental models are widely used in mathematical epidemiology to describe the dynamics of infectious diseases and in mathematical models of population genetics. While the existence of an optimal solution under certain condition can be often proved rigorously, this does not always mean that such a solution is easy to implement in practice. Finding a reasonable approximation can in itself be a challenging research problem.

This Research Topic is devoted to modeling, analysis, and approximation problems whose solutions exploit and explore the theory of partial differential equations. It aims to highlight new analytical tools for use in the modeling of problems arising in applied sciences and practical areas. Researchers are invited to submit articles that investigate the qualitative behavior of weak solutions (removability conditions for singularities), the dependence of the local asymptotic property of these solutions on initial and boundary data, and also the existence of solutions. Contributors are particularly encouraged to focus on anisotropic models: analyzing the preconditions on the strength of the anisotropy, and comparing the analytical estimates for the growth behavior of the solutions near the singularities with the observed growth in numerical simulations. The qualitative analysis and analytical results should be confirmed by the numerically observed solution behavior.

This collection seeks original research papers that present new theoretical tools and expand the established application areas. Possible topics include, but are not limited to:

- modeling of nonlinear processes in anisotropic and inhomogeneous media,
- boundary value problems for linear and quasilinear hyperbolic systems,
- elliptic and parabolic equations of diffusion-absorption structure,
- the nonlinear transmission problem for composite beams,
- hyperbolic models in flow dynamics and viscoelasticity,
- numerical simulation,
- numerical and qualitative analysis,
- approximation theory,
- stochastic PDEs.

This Research Topic welcomes high-quality fundamental, applied, and industry focused research that stresses analytical aspects, novel problems, and their solutions. It aims to provide a high-visibility, open-access publishing outlet for researchers in mathematical analysis, differential equations, numerical analysis, and other mathematical disciplines, while also encouraging collaboration between these disciplines and other related applied fields.

Keywords: boundary value problems, linear and quasilinear hyperbolic systems, elliptic and parabolic anisotropic equations, diffusion-absorption structure, nonlinear transmission problems, composite beams, hyperbolic models, flow dynamics and viscoelasticity

Important note: All contributions to this Research Topic must be within the scope of the section and journal to which they are submitted, as defined in their mission statements. Frontiers reserves the right to guide an out-of-scope manuscript to a more suitable section or journal at any stage of peer review.

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