In this paper, the parabolic problem $$u_t - div(\omega (x) \nabla u)= h(t) f(u) + l(t) g(u)$$ with non-negative initial conditions pertaining to $$C_b({\mathbb {R}}^N)$$ , will be studied, where weight $$\omega $$ is an appropriate function that belongs Muckenhoupt class $$A_{1 \frac{2}{N}}$$ and functions f, g, h l are continuous. The main goal establish global non-global existence of solutio...

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 21 December 2020Accepted: 20 September 2021Published online: 04 January 2022Keywordsenergy-reaction-diffusion systems, cross-diffusion, entropy method, global-in-time existence weak/renormalized solutions, Onsager system, Soret effect, Dufour effectAMS Subject HeadingsPri...

The aim of this work is to model a jet diffusion flame, to show the corresponding proof of existence of solutions, and to present numerical results. The model is based on the flamelet equations for the chemistry and on the mixture fraction for the flow. Numerical tests are carried out for Sandia Flame D and the results are found to compare well with available data found in the literature.

We prove a general finite-dimensional reduction theorem for critical equations of scalar curvature type. Solutions of these equations are constructed as a sum of peaks. The use of this theorem reduces the proof of existence of multi-peak solutions to some test-functions estimates and to the analysis of the interactions of peaks.