Global nonexistence and stability of solutions of inverse problems for a class of Petrovsky systems

Abstract

In this work, we find conditions on data guaranteeing the global nonexistence of solutions to inverse source problems for a class of Petrovsky systems. We also establish asymptotic stability results for the corresponding problems with the opposite sign of power-type nonlinearities and the integral constraint vanishing as time tends to infinity.

Exponential Growth of Solutions for a Variable-Exponent Fourth-Order Viscoelastic Equation With Nonlinear Boundary Feedback

“…Wu and Tsai [31] considered (1.4) and proved that the solution is global in time under some conditions without the relation between m and p. Moreover, similar to [16], they proved that if p > m, the local solution blows up in finite time. (see also [9,27])…”

A Study on the Blow-Up of Solutions for a Lame´ System of Inverse Problem

“…For more information about the concavity argument, we refer the readers to [16][17][18]. In [26] Shahrouzi and Tahamtani by using the same method found conditions on data that guaranteeing the global nonexistence and asymptotic stability results for a class of Petrovsky inverse source problems (see also [22][23][24]27]). Bukhge ǐm et al [7] considered an inverse problem for the stationary elasticity system with constant Lamé coefficients and variable matrix coefficient depending on the spatial variables and frequency.…”

Asymptotic stability and blowup of solutions for a class of viscoelastic inverse problem with boundary feedback

“…Recently, Tahamtani and Shahrouzi studied asymptotic behavior of solutions for the following inverse problem: and showed that the solutions of this problem under some appropriate conditions are stable if α 1 and α 2 being large enough, α 3 ≥0 and ϕ ( t ) tend to zero as time goes to infinity and established a blow‐up result, if α 3 <0 and ϕ ( t ) = k be a constant. For more information about inverse problems, we refer the readers to the works in .…”