On the well-posedness of a nonlinear pseudo-parabolic equation

Abstract fractional linear pseudo-parabolic equations in Banach spaces: well-posedness, regularity, and asymptotic behavior

“…These facts are directly related to the sectorial property of A and in particular to the behavior of z α /(1 + z β ) respect to the sector S θ associated to A. In this regard note that the left-hand side term z γ /(1 + z β ) in (29) does not affect the result, and therefore is avoided hereafter in the proof. Denote z = ρ e iϕ , ρ ≥ 0, and π/2 < ϕ < π.…”

“…In [6,8,11,24,31] the study is extended to semi-linear pseudo-parabolic equations also involving a fractional Laplacian. In [28,29] two different powers of the Laplacian acting separately on u(x, t) and ∂ t u(x, t) are considered, and in [18,23] time fractional derivatives are introduced in the format…”

On the Convergence Result of the Fractional Pseudoparabolic Equation

“…Moreover, when s � 0, we obtain the ordinary pseudoparabolic equation. Both of these equations had been carefully studied by many researchers recently [1][2][3].…”

Long time behavior of solutions for time-fractional pseudo-parabolic equations involving time-varying delays and superlinear nonlinearities

“…Concerning the initial value problem (1.1)-(1.3) without delays, it should be noticed that the linear part of the equation (1.1) is used to describe many different phenomena in physics such as seepage of homogeneous liquids in fissured rocks [23] and the aggregation of populations [21], etc. The existence, stability and blow up in finite time of solutions governed by tFrPPEs and its nonlinear invariants were dealt with in a large number of published investigations; see, e.g., [8,9,17,18,19,25,26,27,32,34]. However, to our knowledge, questions on the global existence and long time behavior of solutions for problem (1.1)- (1.3) have not yet been concerned in the literature.…”