In this work, three types of parabolic heaters with different entrance widths were made and used in the heating experiment.
There have been many kinds of extensions of Fujita's results since then, such as different types of parabolic equations and systems with or without degeneracies or singularities, various geometries of domains, different nonlinear reactions or nonhomogeneous boundary sources, etc.
To the best of the authors' knowledge, although there are many works on several types of parabolic backward problems, the theoretical literature on regularizing the inverse problems for ultraparabolic equations is very scarce.
There are other types of parabolic equations, such as anisotropic diffusion models [1, 2], complex diffusion models [3], fourth order equation models [4, 5], and total variation models [6 8].
Additional to shape deviation already induced by the manufacturing process, deformation due to gravity load is an inevitable factor influencing shape accuracy in all types of parabolic trough collectors.
In this work, a novel type of compound parabolic concentrating photovoltaic/thermal collector with microencapsulated phase change slurry was proposed to solve these problems.
Assume that r > 0. Denote by I the type of minimal parabolic subgroups of G over F n. Fix a Cartan subalgebra h 0 ⊂ g, the corresponding maximal torus T 0 ⊂ G and a basis of the root system Σ ( T 0, G ).
This yields a problem that couples two different model equations (one of hyperbolic type, the other one of parabolic type) through suitable matching conditions at subdomain interfaces.
In order to improve the thermal efficiency, reduce the heat losses and achieve high freezing resistance of the solar device for space heating in cold regions, a new type of serpentine compound parabolic concentrator solar collector is presented in this paper, which is a combination of a compound parabolic concentrator solar collector and a flat plate solar collector.
