Non-Simultaneous Failure of Ice in Front of Multi-Leg Structures

Because the multi-leg jacket structure is the major type of offshore structures in the Bohai Sea, the study of non-simultaneous failure of ice on multi-leg structures is important. However, the non-simultaneous failure has not been considered in engineering design until now, obviously resulting in costly design and notable waste. To resolve this problem, this paper, by means of analysis of experimental data, calculates the coefficient of the non-simultaneous failure for the double-pile structure, the square four-leg structure, the single-line multi-pile structure, and the conical structure, respectively, and provides some reference criteria for engineering design.

Non-simultaneous Blow-up Criteria for Localized Parabolic Equations

This paper deals with blow-up solutions for parabolic equations coupled via localized exponential sources, subject to homogeneous Dirichlet boundary con- ditions. The criteria are proposed to identify simultaneous and non-simultaneous blow-up solutions. The related classification for the four nonlinear parameters in the model is optimal and complete.

THE SIMULTANEOUS AND NON-SIMULTANEOUS BLOW-UP CRITERIA FOR A DIFFUSION SYSTEM

This paper investigates the finite time blow-up of nonnegative solutions for a nonlinear diffusion system with a more complicated source term, which is a product of localized source, local source, and weight function, and complemented by homogeneous Dirichlet boundary conditions. The criteria are proposed to identify simultaneous and nonsimultaneous blow-up solutions. Moreover, the related classification for the four parameters in the model is optimal and complete. The results extend those in Zhang and Yang [12].

Extinction and Non-simultaneous Blow-up of Solutions in Fast Diffusion Equations

In this paper,we deal with some fast di usion equations ut=um+au vp and vt=△v^n+bu^qv^βsubject to null Dirichlet boundary conditions.We prove that every solution vanishes in nite time for pq>(m-α)(n-β),m>αand n>β,where the exact relation of initial data is determined with the aid of some Sobolev Embedding inequalities.If pd<(m-α)(n-β),m>αand n>β,we show the barriers of the initial data which lead to the non-extinction of solutions.For the case pq=(m-α)(n-β),the solutions vanish for small initial data.The results fill in a gap for the case pq<mn in Nonlinear Anal.Real World Appl.4(2013)1931-1937.The coecients a and b play a vital role in the existence of non-extinction weak solution provided that a and b are large enough.At last,we use the scaling methods to determine some exponent regions where one of the components would blow up alone for some suitable initial data.

Critical Quenching Exponents for Heat Equations Coupled with Nonlinear Boundary Flux

We discuss the quenching phenomena for a system of heat equations coupled with nonlinear boundary flux. We determine a critical value for the exponents in the boundary flux, such that only in the super critical case the simultaneous quenching can happen for any solution.

Quenching Estimates for Reaction-diffusion Equations with Nonstandard Growth Conditions

This paper deals with reaction-diffusion equations involving nonstandard growth conditions, subject to homogeneous Neumann boundary conditions. The complete clas- sification is established for simultaneous and non-simultaneous quenching under suitable assumptions on initial data. Moreover, quenching sets and quenching rates are obtained.

Quenching rates for heat equations with coupled singular nonlinear boundary flux

We study finite time quenching for heat equations coupled via singular nonlinear boundary flux. A criterion is proposed to identify the simultaneous and non-simultaneous quenchings. In particular, three kinds of simultaneous quenching rates are obtained for different nonlinear exponent regions and appropriate initial data. This extends an original work by Pablo, Quirós and Rossi for a heat system with coupled inner absorption terms subject to homogeneous Neumann boundary conditions.