With the urgent need to resolve complex behaviors in nonlinear evolution equations,this study makes a contribution by establishing the local existence of solutions for Cauchy problems associated with equations of mixe...With the urgent need to resolve complex behaviors in nonlinear evolution equations,this study makes a contribution by establishing the local existence of solutions for Cauchy problems associated with equations of mixed types.Our primary contribution is the establishment of solution existence,illuminating the dynamics of these complex equations.To tackle this challenging problem,we construct an approximate solution sequence and apply the contraction mapping principle to rigorously prove local solution existence.Our results significantly advance the understanding of nonlinear evolution equations of mixed types.Furthermore,they provide a versatile,powerful approach for tackling analogous challenges across physics,engineering,and applied mathematics,making this work a valuable reference for researchers in these fields.展开更多
We study the distribution limit of a class of stochastic evolution equation driven by an additive-stable Non-Gaussian process in the case of α∈(1,2).We prove that,under suitable conditions,the law of the solution co...We study the distribution limit of a class of stochastic evolution equation driven by an additive-stable Non-Gaussian process in the case of α∈(1,2).We prove that,under suitable conditions,the law of the solution converges weakly to the law of a stochastic evolution equation with an additive Gaussian process.展开更多
Anchoring mechanism and failure characteristics of composite soft rock with weak interface usually exhibit remarkable difference from those in single rock mass.In order to fully understand the reinforcement mechanism ...Anchoring mechanism and failure characteristics of composite soft rock with weak interface usually exhibit remarkable difference from those in single rock mass.In order to fully understand the reinforcement mechanism of composite soft roof in western mining area of China,a mechanical model of composite soft rock with weak interface and rock bolt which considering the transverse shear sliding between different rock layers was established firstly.The anchoring effect was quantified by a factor defined as anchoring effect coefficient and its evolution equation was further deduced based on the deformation relationship and homogenized distribution assumption of stress acting on composite structure.Meanwhile,the numerical simulation model of composite soft rock with shear joint was prompted by finite element method.Then detailed analysis were carried out for the deformation features,stress distribution and failure behavior of rock mass and rock bolt near the joint under transverse load.The theoretical result indicates that the anchoring effect of rock-bolt through weak joint changes with the working status of rock mass and closely relates with the physical and geometric parameters of rock mass and rock bolt.From the numerical results,the bending deformation of rock bolt accurately characterized by Doseresp model is mainly concentrated between two plastic hinges near the shear joint.The maximum tensile and compression stresses distribute in the plastic hinge.However,the maximum shear stress appears at the positions of joint surface.The failure zones of composite rock are produced firstly at the joint surface due to the reaction of rock bolt.The above results laid a theoretical and computational foundation for further study of anchorage failure in composite soft rock.展开更多
基金Supported by the National Natural Science Foundation of China(12201368,62376252)Key Project of Natural Science Foundation of Zhejiang Province(LZ22F030003)Zhejiang Province Leading Geese Plan(2024C02G1123882,2024C01SA100795).
文摘With the urgent need to resolve complex behaviors in nonlinear evolution equations,this study makes a contribution by establishing the local existence of solutions for Cauchy problems associated with equations of mixed types.Our primary contribution is the establishment of solution existence,illuminating the dynamics of these complex equations.To tackle this challenging problem,we construct an approximate solution sequence and apply the contraction mapping principle to rigorously prove local solution existence.Our results significantly advance the understanding of nonlinear evolution equations of mixed types.Furthermore,they provide a versatile,powerful approach for tackling analogous challenges across physics,engineering,and applied mathematics,making this work a valuable reference for researchers in these fields.
基金Supported by the Science and Technology Research Projects of Hubei Provincial Department of Education(B2022077)。
文摘We study the distribution limit of a class of stochastic evolution equation driven by an additive-stable Non-Gaussian process in the case of α∈(1,2).We prove that,under suitable conditions,the law of the solution converges weakly to the law of a stochastic evolution equation with an additive Gaussian process.
基金Projects(51774196,41472280,51578327)supported by the National Natural Science Foundation of ChinaProject(2016M592221)supported by the China Postdoctoral Science FoundationProject(BJRC20160501)supported by the SDUST Young Teachers Teaching Talent Training Plan,China
文摘Anchoring mechanism and failure characteristics of composite soft rock with weak interface usually exhibit remarkable difference from those in single rock mass.In order to fully understand the reinforcement mechanism of composite soft roof in western mining area of China,a mechanical model of composite soft rock with weak interface and rock bolt which considering the transverse shear sliding between different rock layers was established firstly.The anchoring effect was quantified by a factor defined as anchoring effect coefficient and its evolution equation was further deduced based on the deformation relationship and homogenized distribution assumption of stress acting on composite structure.Meanwhile,the numerical simulation model of composite soft rock with shear joint was prompted by finite element method.Then detailed analysis were carried out for the deformation features,stress distribution and failure behavior of rock mass and rock bolt near the joint under transverse load.The theoretical result indicates that the anchoring effect of rock-bolt through weak joint changes with the working status of rock mass and closely relates with the physical and geometric parameters of rock mass and rock bolt.From the numerical results,the bending deformation of rock bolt accurately characterized by Doseresp model is mainly concentrated between two plastic hinges near the shear joint.The maximum tensile and compression stresses distribute in the plastic hinge.However,the maximum shear stress appears at the positions of joint surface.The failure zones of composite rock are produced firstly at the joint surface due to the reaction of rock bolt.The above results laid a theoretical and computational foundation for further study of anchorage failure in composite soft rock.
