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Blowup of Volterra Integro-Differential Equations and Applications to Semi-Linear Volterra Diffusion Equations

  • Zhanwen Yang (a1), Tao Tang (a2) and Jiwei Zhang (a3)
Abstract
Abstract

In this paper, we discuss the blowup of Volterra integro-differential equations (VIDEs) with a dissipative linear term. To overcome the fluctuation of solutions, we establish a Razumikhin-type theorem to verify the unboundedness of solutions. We also introduce leaving-times and arriving-times for the estimation of the spending-times of solutions to ∞. Based on these two typical techniques, the blowup and global existence of solutions to VIDEs with local and global integrable kernels are presented. As applications, the critical exponents of semi-linear Volterra diffusion equations (SLVDEs) on bounded domains with constant kernel are generalized to SLVDEs on bounded domains and ℝ N with some local integrable kernels. Moreover, the critical exponents of SLVDEs on both bounded domains and the unbounded domain ℝ N are investigated for global integrable kernels.

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Corresponding author
*Corresponding author. Email addresses: yangzhan_wen@126.com (Z. Yang), tangt@sustc.edu.cn (T. Tang), jwzhang@csrc.ac.cn (J. Zhang)
References
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Numerical Mathematics: Theory, Methods and Applications
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