Nonexistence of global solutions for an inhomogeneous pseudo-parabolic equation
Borikhanov M.B. Torebek B.T.
December 2022Elsevier Ltd
Applied Mathematics Letters
2022#134
In the present paper, we study an inhomogeneous pseudo-parabolic equation with nonlocal nonlinearity ut−kΔut−Δu=I0+γ(|u|p)+ω(x),(t,x)∈(0,∞)×RN,where p>1,k≥0, ω(x)≠0 and I0+γ is the left Riemann–Liouville fractional integral of order γ∈(0,1). Based on the test function method, we have proved the blow-up result for the critical case γ=0,p=pc for N≥3, which answers an open question posed by Zhou (2020), and in particular when k=0 it improves the result obtained by Bandle et al. (2000). An interesting fact is that in the case γ>0, the problem does not admit global solutions for any p>1 and ∫Rω(x)dx>0.
Critical exponent , Nonexistence of global solution , Semilinear pseudo-parabolic equation
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Khoja Akhmet Yassawi International Kazakh–Turkish University, Sattarkhanov ave., 29, Turkistan, 161200, Kazakhstan
Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Belgium
Institute of Mathematics and Mathematical Modeling, 125 Pushkin str., Almaty, 050010, Kazakhstan
Khoja Akhmet Yassawi International Kazakh–Turkish University
Department of Mathematics: Analysis
Institute of Mathematics and Mathematical Modeling
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