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Global solutions and blow up solutions to a class of pseudo-parabolic equations with nonlocal term

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  • Zhu, Xiaoli
  • Li, Fuyi
  • Li, Yuhua

Abstract

In this paper, we investigate an initial boundary value problem to a class of pseudo-parabolic partial differential equations with Newtonian nonlocal term. First, the local existence and uniqueness of a weak solution is established. In virtue of the energy functional and the related Nehari manifold, we also describe the exponent decay behavior and the blow up phenomenon of weak solutions with different kinds of initial data. Our second conclusion states that some solutions starting in a potential well exist globally, whereas solutions with suitable initial data outside the potential well must blow up. Furthermore, the instability of a ground state equilibrium solution is studied.

Suggested Citation

  • Zhu, Xiaoli & Li, Fuyi & Li, Yuhua, 2018. "Global solutions and blow up solutions to a class of pseudo-parabolic equations with nonlocal term," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 38-51.
    • Handle: RePEc:eee:apmaco:v:329:y:2018:i:c:p:38-51
    DOI: 10.1016/j.amc.2018.02.003
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    Cited by:

    1. Can, Nguyen Huu & Zhou, Yong & Tuan, Nguyen Huy & Thach, Tran Ngoc, 2020. "Regularized solution approximation of a fractional pseudo-parabolic problem with a nonlinear source term and random data," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    2. Phuong, Nguyen Duc & Tuan, Nguyen Huy & Hammouch, Zakia & Sakthivel, Rathinasamy, 2021. "On a pseudo-parabolic equations with a non-local term of the Kirchhoff type with random Gaussian white noise," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).

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