Global existence, asymptotic behavior and blowup of solutions for a class of nonlinear wave equations with dissipative term

AbstractThe paper studies the global existence, asymptotic behavior and blowup of solutions to the initial boundary value problem for a class of nonlinear wave equations with dissipative term. It proves that under rather mild conditions on nonlinear terms and initial data the above-mentioned problem admits a global weak solution and the solution decays exponentially to zero as t→+∞, respectively, in the states of large initial data and small initial energy. In particular, in the case of space dimension N=1, the weak solution is regularized to be a unique generalized solution. And if the conditions guaranteeing the global existence of weak solutions are not valid, then under the opposite conditions, the solutions of above-mentioned problem blow up in finite time. And an example is given

Blowup of solutions for improved Boussinesq type equation

AbstractThe paper studies the existence and uniqueness of local solutions and the blowup of solutions to the initial boundary value problem for improved Boussinesq type equation utt−uxx−uxxtt=σ(u)xx. By a Galerkin approximation scheme combined with the continuation of solutions step by step and the Fourier transform method, it proves that under rather mild conditions on initial data, the above-mentioned problem admits a unique generalized solution u∈W2,∞([0,T];H2(0,1)) as long as σ∈C2(R). In particular, when σ(s)=asp, where a≠0 is a real number and p>1 is an integer, specially a<0 if p is an odd number, the solution blows up in finite time. Moreover, two examples of blowup are obtained numerically

Cauchy problem for the multi-dimensional Boussinesq type equation

AbstractThe paper studies the existence and non-existence of global weak solutions to the Cauchy problem for the multi-dimensional Boussinesq type equation utt−Δu+Δ2u=Δσ(u). It proves that the Cauchy problem admits a global weak solution under the assumptions that σ∈C(R), σ(s) is of polynomial growth order, say p (>1), either 0⩽σ(s)s⩽β∫0sσ(τ)dτ, s∈R, where β>0 is a constant, or the initial data belong to a potential well. And the weak solution is regularized and the strong solution is unique when the space dimension N=1. In contrast, any weak solution of the Cauchy problem blows up in finite time under certain conditions. And two examples are shown

Finite element analysis of mechanical behavior of concrete-filled square steel tube short columns with inner I-shaped CFRP profiles subjected to bi-axial eccentric load

[EN] The concrete-filed square steel tube with inner I-shaped CFRP profiles short columns under bi-axial eccentric load were investigated by the finite element analysis software ABAQUS. The working mechanism of the composite columns which is under bi-axial eccentric load are investigated by using the stress distribution diagram of steel tube concrete and the I-shaped CFRP profiles. In this paper, the main parameters; eccentric ratio, steel ratio, steel yield strength, concrete compressive strength and CFRP distribution rate of the specimens were investigated to know the mechanical behavior of them. The interaction between the steel tube and the concrete interface at different characteristic points of the composite columns were analyzed. The results showed that the ultimate bearing capacity of the concrete-filed square steel tube with inner I-shaped CFRP profiles short columns under bi-axial eccentric load decrease with the increase of eccentric ratio, the ultimate bearing capacity of the composite columns increase with the increase of steel ratio, steel yield strength, concrete compressive strength and CFRP distribution rate. The contact pressure between the steel tube and the concrete decreased from the corner zone to the flat zone, and the contact pressure decreased from the mid-height cross section to other sections.Li, G.; Zhan, Z.; Yang, Z.; Yang, Y. (2018). Finite element analysis of mechanical behavior of concrete-filled square steel tube short columns with inner I-shaped CFRP profiles subjected to bi-axial eccentric load. En Proceedings of the 12th International Conference on Advances in Steel-Concrete Composite Structures. ASCCS 2018. Editorial Universitat Politècnica de València. 259-266. https://doi.org/10.4995/ASCCS2018.2018.6996OCS25926

Cooperative work behavior of high strength concrete-filled square high strength tubular stub columns with inner I-shaped CFRP under axial compression

[EN] The finite element software ABAQUS was used to analyze 22 high strength concrete-filled square high strength tubular short columns with inner I-shaped CFRP, all analysis results based on the finite element analysis data, six characteristic points were defined in the load-longitudinal strain curve of composite columns. The shared load of core concrete, square steel tube and inner I-shaped CFRP at different height sections of typical specimen corresponding to each characteristic point were analyzed and the cooperative work behavior of inner I-shaped CFRP, square steel tube and core concrete was analyzed. The results show that the existence of the inner I-shaped CFRP can effectively improve the ultimate bearing capacity composite columns, the middle region I-shaped CFRP sharing more longitudinal load than the end region CFRP and the shared load of concrete at the end region section is bigger than that of middle region section, before the CFRP brittle failure. The longitudinal load of square steel tube does not change with the change of the cross-section height.Li, G.; Yang, Y.; Yang, Z.; Zhan, Z. (2018). Cooperative work behavior of high strength concrete-filled square high strength tubular stub columns with inner I-shaped CFRP under axial compression. En Proceedings of the 12th International Conference on Advances in Steel-Concrete Composite Structures. ASCCS 2018. Editorial Universitat Politècnica de València. 281-288. https://doi.org/10.4995/ASCCS2018.2018.6999OCS28128