Existence and Blow-Up of Solutions to a Class of Time-Space Fractional Pseudo-Parabolic Equations

CHEN Yeming; LI Yaning

doi:10.21656/1000-0887.450217

Volume 46 Issue 11

Nov. 2025

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CHEN Yeming, LI Yaning. Existence and Blow-Up of Solutions to a Class of Time-Space Fractional Pseudo-Parabolic Equations[J]. Applied Mathematics and Mechanics, 2025, 46(11): 1480-1490. doi: 10.21656/1000-0887.450217

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Existence and Blow-Up of Solutions to a Class of Time-Space Fractional Pseudo-Parabolic Equations

doi: 10.21656/1000-0887.450217

CHEN Yeming,
LI Yaning^,

School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, P.R.China

Funds:

The National Science Foundation of China(11801276)

Received Date: 2024-07-17
Rev Recd Date: 2024-10-10

Available Online: 2025-12-05

Abstract

Abstract

The effects of the inhomogeneity on the existence and finite time blow-up of solutions to a class of time-space fractional pseudo-parabolic equations were analyzed. Firstly, the local existence of the mild solution was obtained with the fixed-point theorem. By means of the test function method, the solutions' finite-time blow-up was educed under certain conditions. The global existence of the solution to the equation was proved under suitable initial data and inhomogeneous terms. The findings extend the corresponding solution results of integral-order pseudo-parabolic equations, but differ from those of the time-space fractional pseudo-parabolic equations with zero inhomogeneous terms, and show the effects of inhomogeneous terms on the existence and blow-up of the solutions.
- time-space fractional pseudo-parabolic equation,
- mild solution,
- local existence,
- blow-up,
- global existence

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References(17)

References

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