[PDF] Top 20 Existence and blow up of solutions to a Petrovsky equation with memory and nonlinear source term

... weak solutions under some appropriate assumptions on the function g and blow-up behavior of ...the existence of solutions, we use the Faedo-Galerkin method and to get the ... See full document

... parabolic equation with time-integral term does not seem to be so much investigated as nonlocal equations with space-integral ...a memory term has some difficulties in proving the ... See full document

... local existence theorem and show, for some appropriate assumption on g and the initial data, that this solution is global with energy which decays exponentially under the potential ...time blow-up ... See full document

... global existence, blow-up, and energy decay of solutions for this type of problems involving a finite history memory term has attracted much attention; see [3–12] and the ... See full document

... conditions than those in [, ]), that the solution is global and decays uniformly (expo- nentially or polynomially depending on the decay rate of the relaxation function g) if the initial data is small enough. For ... See full document

... the maximum positive solution and completely classified all possible positive solutions. Later, Lair [27], Cîrstea and Rădulescu [10], and Tao and Zhang [46] further investigated the existence of entire ... See full document

... on nonlinear terms, they acquired the existence and uniform decay of ...without memory source term, we point out the work [6] of Cavalcanti et ...following equation with boundary ... See full document

... the blow-up time if blow-up occurs, or else t ∗ = ...cold source function, g is the heat-conduction function transmitting into interior of Ω from the boundary of ... See full document

... the blow-up singularity of a semilinear parabolic equation with nonlinear memory both in the reaction term and the boundary ...the existence of a blow-up ... See full document

... local existence for a generalized solution of the mixed problem un- der consideration by combining generalized contracted mapping principle and Schauder’s fixed point principle and then proved the global ... See full document

... global existence for arbitrary initial data (see ...and nonlinear source has been first considered by Levine [7] ...that solutions with negative initial energy blew up in fi- nite ... See full document

... with memory term act- ing in the boundary or in the domain, there are numerous results related to asymptotic behavior of ...the existence and uniform decay of strong solutions of wave ... See full document

... viscoelastic term 0 t g(t − τ )d τ , the equations are known as the wave ...wave equation subject to nonlinear boundary damp- ing has been investigated by the authors Cavalcanti et ...to blow ... See full document

... be nonlinear and it should have enough degrees of freedom to display torsional ...the nonlinear behavior of the suspension bridge is well established, see [1, 4, 11, 18, ... See full document

... plate equation have been studied by numerous authors, see ...semilinear Petrovsky equation with the damping and the source term, showed that the solution blows up in finite time ... See full document

... the blow-up problems of the positive solutions to a nonlinear parabolic equation with nonlocal source and nonlocal boundary ...The blow-up and global ... See full document

... In recent years, some researchers obtained the finite time blow-up results for different kinds of evolution equations with initial data at arbitrary high energy level. In [16], Todor- ova and Vitillaro ... See full document

... local existence of weak and strong solutions of problem ...global existence of the strong solutions, while in Section  we prove the blow-up phenomenon of strong solutions ... See full document

... This motivates us to further study the blow-up solutions of Eq. (1.1) in the following sense: Under what conditions will the waves become unstable to collapse (blow-up)? Un- der what ... See full document

... The nonlinear beam equation is a class of fourth-order partial differential equations ap- pearing in different physical settings (see [26, 27] for a review), and it models the weak interactions of dispersive ... See full document