Existence and Blow-Up Phenomena of Solutions to Heat Equations With Variable Coefficients Under Nonlinear Boundary Conditions

LI Yuanfei; XIAO Shengzhong; CHEN Xuejiao

doi:10.21656/1000-0887.410091

Volume 42 Issue 1

Jan. 2021

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LI Yuanfei, XIAO Shengzhong, CHEN Xuejiao. Existence and Blow-Up Phenomena of Solutions to Heat Equations With Variable Coefficients Under Nonlinear Boundary Conditions[J]. Applied Mathematics and Mechanics, 2021, 42(1): 92-101. doi: 10.21656/1000-0887.410091

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Existence and Blow-Up Phenomena of Solutions to Heat Equations With Variable Coefficients Under Nonlinear Boundary Conditions

doi: 10.21656/1000-0887.410091

¹Department of Applied Mathematics, Huashang College, Guangdong University of Finance & Economics, Guangzhou 511300, P.R.China;²Guangdong AIB Polytechnic, Guangzhou 510507, P.R.China

Received Date: 2020-02-16
Publish Date: 2021-01-01

Abstract

Abstract

Under nonlinear boundary conditions, the heat equations with variable coefficients defined on Ω were considered, with Ω∝R^N(N≥2) as a bounded convex region. By means of the technique of differential inequalities, the conditions under which the blowup will definitely occur were derived and the upper bound of the blowup time was determined. Meanwhile, with certain restrictions on the nonlinear terms, the global existence of the solution was obtained. At the blowup moment, the lower bound of the blowup time was also got.
- heat equation,
- global solution,
- blowup,
- differential inequality

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References

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