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Cauchy problems of pseudo-parabolic equations with inhomogeneous terms

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Abstract

This paper deals with Cauchy problems of pseudo-parabolic equations with inhomogeneous terms. The aim of the paper is to study the influence of the inhomogeneous term on the asymptotic behavior of solutions. We at first determine the critical Fujita exponent and then give the secondary critical exponent on the decay asymptotic behavior of an initial value at infinity. Furthermore, the precise estimate of life span for the blow-up solution is obtained. Our results show that the asymptotic behavior of solutions is seriously affected by the inhomogeneous term.

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  1. College of Mathematic and Information, China West Normal University, Nanchong, 637009, People’s Republic of China

    Zhongping Li & Wanjuan Du

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  1. Zhongping Li
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  2. Wanjuan Du
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Correspondence to Zhongping Li.

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Li, Z., Du, W. Cauchy problems of pseudo-parabolic equations with inhomogeneous terms. Z. Angew. Math. Phys. 66, 3181–3203 (2015). https://doi.org/10.1007/s00033-015-0558-2

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  • DOI: https://doi.org/10.1007/s00033-015-0558-2

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