Blow up of solutions of pseudoparabolic equations

Abstract

We obtain sufficient conditions for the blow up of solutions of the initial-boundary value problem for nonlinear pseudoparabolic equation involving nonlinear convective term.

General decay and blow‐up results for a nonlinear pseudoparabolic equation with Robin–Dirichlet conditions

“…With ν > 0, α > 0, x ∈ [0, 1], t ≥ 0, the model has the form () was also investigated earlier by Bona and Dougalis 36 where uniqueness, global existence, and continuous dependence of solutions on initial and boundary data were established and the solutions were shown to depend continuously on ν ≥ 0 and on α > 0. The results obtained in Amick et al 35 were developed by many authors, such as by Zhang for equations of the form where m ≥ 0, see Meyvaci 16 and Zhang 32 …”

“…The pseudoparabolic equation with the initial condition and with the different boundary conditions, has been extensively studied by many authors, see for example, previous studies 1‐32,33,34 among others and the references given therein. In these works, many results about existence, asymptotic behavior, blow‐up, and decay of solutions were obtained.…”

Quenching Time Estimates for Semilinear Parabolic Equations Controlled by Two Absorption Sources in Control System

“…We change the exponents of both two absorption sources such that the two terms have a large enough gaps in the sense of growth order, in order to reveal and compare the importance of the two factors acting on the behavior of the quenching phenomena, which are the number of the absorption source terms and the exponents of these terms. The results obtained in the preset paper suggests the dominant influence of the exponents of the absorption terms comparing the number of them, which is not only different from the classical heat equation with nonlinear power-type external force [12,13], but also different from the nonlinearities and their corresponding behaviours and affects in other models [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30].…”

Some sharp results about the global existence and blowup of solutions to a class of pseudo-parabolic equations

“…Furthermore, as in the study of the parabolic equation, the blowup of solutions to pseudo-parabolic equations has also been extensively investigated; see, for example, [2,12,14,17,25]. For example, it can be derived from [14,theorem II] that for IBVP (1.1) the negative initial energy (J(u 0 ) < 0) is a sufficient condition for finite time blowup of the solution, and in [17] Meyvaci obtained sufficient conditions for the blowup of solutions of the IBVP for a class of nonlinear pseudo-parabolic equations involving a nonlinear convective term. He proved that if the initial data u 0 has a large norm in some suitable space, then the solution blows up at a finite time.…”