Blow up Problem of Reaction Diffusion Equation with Time-dependent Coefficients
School of Science, Dalian Jiaotong University, Dalian 116028, China
| Abstract: | Partial differential equations are used to analyze and solve practical problems in real life by establishing mathematical models. As an important part of partial differential equations, reaction diffusion equations not only have theoretical significance, but also have more practical physical significance, especially in the fields of physics, chemistry, medicine, bioscience, and infectious disease. In real life, The pyrogen function is not only related to temperature, but also to the time switching function. This paper considers the blowup problem of a divergence type reaction diffusion equation with homogeneous Neumann boundary conditions and time-dependent coefficients. The difficulty lies in finding the influence of time-dependent coefficients and the relationship between the internal absorption term and the boundary source to determine the blowup of the solution. By constructing appropriate energy functional and defining appropriate auxiliary functions, the method of convexity argumentation is used, And combined with differential inequality estimation and a series of inequalities such as Young, the blow up time of the reaction diffusion equation was calculated under appropriate assumptions. |
| Keywords: | Reaction Diffusion Equation; Time Dependent Coefficient; Burst Time |
| DOI: | 10.57237/j.wjms.2023.02.001 |
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Received: 6 July 2023
Accepted: 31 August 2023
Published Online: 8 September 2023
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