Blow-up solutions to the fractional solid fuel ignition model

Authors

Nguyen Dinh Huy Department of Mathematics, Faculty of Applied Science, Ho Chi Minh City University of Technology (HCMUT), 268 Ly Thuong Kiet Street, District 10, Ho Chi Minh City, Vietnam https://orcid.org/0000-0002-3755-0757
Anh Tuan Nguyen Division of Applied Mathematics, Science and Technology Advanced Institute, Van Lang University, Ho Chi Minh City, Vietnam https://orcid.org/0000-0002-8757-9742

https://doi.org/10.61383/ejam.20231126

Keywords:

Caputo-Fabrizio, fractional equation, exponential nonlinearity

Abstract

In this study, we investigate a time fractional parabolic equation with Caputo-Fabrizio derivative and a pure exponential source term. The model can be seen as a modified version of a solid fuel ignition by considering delay effects. Because of the bad behavior of the source term, the common Banach fixed point theorem is not suitable to be applied. Therefore, we approach by an iteration method in which we find a supersolution to the problem. Then, the monotony of approximating solutions implies the existence of a mild solution. Furthermore, we show that if the given initial data is sufficiently large in term of norm measure, the corresponding solution will blow up in a finite time. Main techniques of the work are mainly based on calculations related to explicit formulas of solution operator derived from eigenpair of Helmholtz's equation and Sobolev embeddings between Hilbert scale spaces.

References

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Published

2023 May 07

How to Cite

[1]

N. D. Huy and A. T. Nguyen, “ Blow-up solutions to the fractional solid fuel ignition model”, Electron. J. Appl. Math., vol. 1, no. 1, pp. 30–39, May 2023.