In this article, we consider a two-component nonlinear shallow water system, which includes the famous 2-component Camassa-Holm and Degasperis-Procesi equations as special cases. The local well-posedess for this equat...In this article, we consider a two-component nonlinear shallow water system, which includes the famous 2-component Camassa-Holm and Degasperis-Procesi equations as special cases. The local well-posedess for this equations is established. Some sufficient conditions for blow-up of the solutions in finite time are given. Moreover, by separation method, the self-similar solutions for the nonlinear shallow water equations are obtained, and which local or global behavior can be determined by the corresponding Emden equation.展开更多
Blow-up phenomena for solutions of some nonlinear parabolic systems with time dependent coefficients are investigated. Both lower and upper bounds for the blow-up time are derived when blow-up occurs.
By means of maximum principle for nonlinear hyperbolic systems, the results given by HSIAO Ling and D. Serre was improved for Cauchy problem of compressible adiabatic flow through porous media, and a complete result o...By means of maximum principle for nonlinear hyperbolic systems, the results given by HSIAO Ling and D. Serre was improved for Cauchy problem of compressible adiabatic flow through porous media, and a complete result on the global existence and the blow-up phenomena of classical solutions of these systems. These results show that the dissipation is strong enough to preserve the smoothness of ‘small ’ solution.展开更多
We focus on the blow-up phenomena of Cauchy problem for the Camassa-Holm equation. Blow-up can occur only in the form of wave-breaking, i.e. the solution is bounded but its slope becomes unbounded in finite time. We p...We focus on the blow-up phenomena of Cauchy problem for the Camassa-Holm equation. Blow-up can occur only in the form of wave-breaking, i.e. the solution is bounded but its slope becomes unbounded in finite time. We proved that there is such a point that its slope becomes infinite exactly at breaking time. We also gave the precise blow-up rate and the blow-up set.展开更多
Laser-accelerated high-flux-intensity heavy-ion beams are important for new types of accelerators.A particle-in-cell program(Smilei) is employed to simulate the entire process of Station of Extreme Light(SEL) 100 PW l...Laser-accelerated high-flux-intensity heavy-ion beams are important for new types of accelerators.A particle-in-cell program(Smilei) is employed to simulate the entire process of Station of Extreme Light(SEL) 100 PW laser-accelerated heavy particles using different nanoscale short targets with a thickness of 100 nm Cr, Fe, Ag, Ta, Au, Pb, Th and U, as well as 200 nm thick Al and Ca. An obvious stratification is observed in the simulation. The layering phenomenon is a hybrid acceleration mechanism reflecting target normal sheath acceleration and radiation pressure acceleration, and this phenomenon is understood from the simulated energy spectrum,ionization and spatial electric field distribution. According to the stratification, it is suggested that high-quality heavy-ion beams could be expected for fusion reactions to synthesize superheavy nuclei. Two plasma clusters in the stratification are observed simultaneously, which suggest new techniques for plasma experiments as well as thinner metal targets in the precision machining process.展开更多
In this paper, we investigate a blow-up phenomenon for a semilinear parabolic system on locally finite graphs. Under some appropriate assumptions on the curvature condition CDE’(n,0), the polynomial volume growth of ...In this paper, we investigate a blow-up phenomenon for a semilinear parabolic system on locally finite graphs. Under some appropriate assumptions on the curvature condition CDE’(n,0), the polynomial volume growth of degree m, the initial values, and the exponents in absorption terms, we prove that every non-negative solution of the semilinear parabolic system blows up in a finite time. Our current work extends the results achieved by Lin and Wu (Calc Var Partial Differ Equ, 2017, 56: Art 102) and Wu (Rev R Acad Cien Serie A Mat, 2021, 115: Art 133).展开更多
This paper is concerned with the finite time blow-up phenomena for the vector nonlinear Schrdinger equations with a magnetic field which describe the spontaneous generation of a magnetic field in a cold plasma in the ...This paper is concerned with the finite time blow-up phenomena for the vector nonlinear Schrdinger equations with a magnetic field which describe the spontaneous generation of a magnetic field in a cold plasma in the subsonic limit. After obtaining some a priori estimates,we prove under certain natural conditions that the solutions to the Cauchy problem of the vector nonlinear Schrdinger equations in two and three spatial dimensions blow up in a finite time. Assuming that a solution to the aforementioned vector nonlinear Schrdinger equations is radially symmetric with respect to spatial variables x,we show that if the initial energy is non-positive,then the solution blows up in three dimensions in a finite time.展开更多
Despite the enormous interest in inorganic/polymer composite solid-state electrolytes(CSEs)for solid-state batteries(SSBs),the underlying ion transport phenomena in CSEs have not yet been elucidated.Here,we address th...Despite the enormous interest in inorganic/polymer composite solid-state electrolytes(CSEs)for solid-state batteries(SSBs),the underlying ion transport phenomena in CSEs have not yet been elucidated.Here,we address this issue by formulating a mechanistic understanding of bi-percolating ion channels formation and ion conduction across inorganic-polymer electrolyte interfaces in CSEs.A model CSE is composed of argyrodite-type Li_6PS_5Cl(LPSCl)and gel polymer electrolyte(GPE,including Li~+-glyme complex as an ion-conducting medium).The percolation threshold of the LPSCl phase in the CSE strongly depends on the elasticity of the GPE phase.Additionally,manipulating the solvation/desolvation behavior of the Li~+-glyme complex in the GPE facilitates ion conduction across the LPSCl-GPE interface.The resulting scalable CSE(area=8×6(cm×cm),thickness~40μm)can be assembled with a high-mass-loading LiNi_(0.7)Co_(0.15)Mn_(0.15)O_(2)cathode(areal-mass-loading=39 mg cm~(-2))and a graphite anode(negative(N)/positive(P)capacity ratio=1.1)in order to fabricate an SSB full cell with bi-cell configuration.Under this constrained cell condition,the SSB full cell exhibits high volumetric energy density(480 Wh L_(cell)~(-1))and stable cyclability at 25℃,far exceeding the values reported by previous CSE-based SSBs.展开更多
We investigate the p-Laplace heat equation ut-△_(p)u=ζ(t)f(u)in a bounded smooth domain.Using differential-inequality arguments,we prove blow-up results under suitable conditions onζ,f,and the initial datum u_(0).W...We investigate the p-Laplace heat equation ut-△_(p)u=ζ(t)f(u)in a bounded smooth domain.Using differential-inequality arguments,we prove blow-up results under suitable conditions onζ,f,and the initial datum u_(0).We also give an upper bound for the blow-up time in each case.展开更多
We investigate the initial boundary value problem of some semilinear pseudo-parabolic equations with Newtonian nonlocal term.We establish a lower bound for the blow-up time if blow-up does occur.Also both the upper bo...We investigate the initial boundary value problem of some semilinear pseudo-parabolic equations with Newtonian nonlocal term.We establish a lower bound for the blow-up time if blow-up does occur.Also both the upper bound for T and blow up rate of the solution are given when J(u 0)<0.Moreover,we establish the blow up result for arbitrary initial energy and the upper bound for T.As a product,we refine the lifespan when J(u 0)<0.展开更多
We consider the blow-up solutions to the following coupled nonlinear Schr¨odinger equations{iu_(t)+Δu+(|u|^(2p)+|u|^(p−1)|v|^(p+1))u=0,iv_(t)+Δv+(|v|^(2p)+|v|^(p−1)|u|^(p+1))v=0,u(0,x)=u0(x),v(0,x)=v0(x),x 2 R ...We consider the blow-up solutions to the following coupled nonlinear Schr¨odinger equations{iu_(t)+Δu+(|u|^(2p)+|u|^(p−1)|v|^(p+1))u=0,iv_(t)+Δv+(|v|^(2p)+|v|^(p−1)|u|^(p+1))v=0,u(0,x)=u0(x),v(0,x)=v0(x),x 2 R N,t0.On the basis of the conservation of mass and energy,we establish two sufficient conditions to obtain the existence of a blow-up for radially symmetric solutions.These results improve the blow-up result of Li and Wu[10]by dropping the hypothesis of finite variance((|x|u_(0),|x|v_(0))∈ L^(2)(R^(N))×L^(2)(R^(N))).展开更多
Let?denote a smooth,bounded domain in R^(N)(N≥2).Suppose that g is a nondecreasing C^(1)positive function and assume that b(x)is continuous and nonnegative inΩ,and that it may be singular on■Ω.In this paper,we pro...Let?denote a smooth,bounded domain in R^(N)(N≥2).Suppose that g is a nondecreasing C^(1)positive function and assume that b(x)is continuous and nonnegative inΩ,and that it may be singular on■Ω.In this paper,we provide sufficient and necessary conditions on the existence of boundary blow-up solutions to the p-Laplacian problem△_(p)u=b(x)g(u)for x∈Ω,u(x)→+∞as dist(x,■Ω)→0.The estimates of such solutions are also investigated.Moreover,when b has strong singularity,the nonexistence of boundary blow-up(radial)solutions and infinitely many radial solutions are also considered.展开更多
基金supported by NSF of China (11071266)partially supported by Scholarship Award for Excellent Doctoral Student granted by Ministry of Educationpartially supported by the found of Chongqing Normal University (13XLB006)
文摘In this article, we consider a two-component nonlinear shallow water system, which includes the famous 2-component Camassa-Holm and Degasperis-Procesi equations as special cases. The local well-posedess for this equations is established. Some sufficient conditions for blow-up of the solutions in finite time are given. Moreover, by separation method, the self-similar solutions for the nonlinear shallow water equations are obtained, and which local or global behavior can be determined by the corresponding Emden equation.
文摘Blow-up phenomena for solutions of some nonlinear parabolic systems with time dependent coefficients are investigated. Both lower and upper bounds for the blow-up time are derived when blow-up occurs.
文摘By means of maximum principle for nonlinear hyperbolic systems, the results given by HSIAO Ling and D. Serre was improved for Cauchy problem of compressible adiabatic flow through porous media, and a complete result on the global existence and the blow-up phenomena of classical solutions of these systems. These results show that the dissipation is strong enough to preserve the smoothness of ‘small ’ solution.
基金Supported by the National Natural Science Foun-dation of China (10131050) Science and Technology Committee of Shanghai ,China (03JC14013)
文摘We focus on the blow-up phenomena of Cauchy problem for the Camassa-Holm equation. Blow-up can occur only in the form of wave-breaking, i.e. the solution is bounded but its slope becomes unbounded in finite time. We proved that there is such a point that its slope becomes infinite exactly at breaking time. We also gave the precise blow-up rate and the blow-up set.
基金support from the Strategic Priority Research Program of the Chinese Academy of Sciences (No.XDB34030000)the National Key R & D Program of China (No.2022YFA1602404)+2 种基金National Natural Science Foundation of China (No. U1832129)the Youth Innovation Promotion Association of the Chinese Academy of Sciences (No.2017309)the Program for Innovative Research Team (in Science and Technology) in University of Henan Province of China (No.21IRTSTHN011)。
文摘Laser-accelerated high-flux-intensity heavy-ion beams are important for new types of accelerators.A particle-in-cell program(Smilei) is employed to simulate the entire process of Station of Extreme Light(SEL) 100 PW laser-accelerated heavy particles using different nanoscale short targets with a thickness of 100 nm Cr, Fe, Ag, Ta, Au, Pb, Th and U, as well as 200 nm thick Al and Ca. An obvious stratification is observed in the simulation. The layering phenomenon is a hybrid acceleration mechanism reflecting target normal sheath acceleration and radiation pressure acceleration, and this phenomenon is understood from the simulated energy spectrum,ionization and spatial electric field distribution. According to the stratification, it is suggested that high-quality heavy-ion beams could be expected for fusion reactions to synthesize superheavy nuclei. Two plasma clusters in the stratification are observed simultaneously, which suggest new techniques for plasma experiments as well as thinner metal targets in the precision machining process.
基金supported by the Zhejiang Provincial Natural Science Foundation of China(LY21A010016)the National Natural Science Foundation of China(11901550).
文摘In this paper, we investigate a blow-up phenomenon for a semilinear parabolic system on locally finite graphs. Under some appropriate assumptions on the curvature condition CDE’(n,0), the polynomial volume growth of degree m, the initial values, and the exponents in absorption terms, we prove that every non-negative solution of the semilinear parabolic system blows up in a finite time. Our current work extends the results achieved by Lin and Wu (Calc Var Partial Differ Equ, 2017, 56: Art 102) and Wu (Rev R Acad Cien Serie A Mat, 2021, 115: Art 133).
基金supported by National Natural Science Foundation of China (Grant Nos. 11171241, 10801102, 11071177)
文摘This paper is concerned with the finite time blow-up phenomena for the vector nonlinear Schrdinger equations with a magnetic field which describe the spontaneous generation of a magnetic field in a cold plasma in the subsonic limit. After obtaining some a priori estimates,we prove under certain natural conditions that the solutions to the Cauchy problem of the vector nonlinear Schrdinger equations in two and three spatial dimensions blow up in a finite time. Assuming that a solution to the aforementioned vector nonlinear Schrdinger equations is radially symmetric with respect to spatial variables x,we show that if the initial energy is non-positive,then the solution blows up in three dimensions in a finite time.
基金the Basic Science Research Program(2018M3D1A1058744,2021R1A5A6002853,2021R1A2B5B03001615,and 2022M3J1A1085397)through the National Research Foundation of Korea(NRF)grant by the Korean Government(MSIT)provided by KISTI(KSC-2020-CRE-0301)supported by the Hyundai NGV program。
文摘Despite the enormous interest in inorganic/polymer composite solid-state electrolytes(CSEs)for solid-state batteries(SSBs),the underlying ion transport phenomena in CSEs have not yet been elucidated.Here,we address this issue by formulating a mechanistic understanding of bi-percolating ion channels formation and ion conduction across inorganic-polymer electrolyte interfaces in CSEs.A model CSE is composed of argyrodite-type Li_6PS_5Cl(LPSCl)and gel polymer electrolyte(GPE,including Li~+-glyme complex as an ion-conducting medium).The percolation threshold of the LPSCl phase in the CSE strongly depends on the elasticity of the GPE phase.Additionally,manipulating the solvation/desolvation behavior of the Li~+-glyme complex in the GPE facilitates ion conduction across the LPSCl-GPE interface.The resulting scalable CSE(area=8×6(cm×cm),thickness~40μm)can be assembled with a high-mass-loading LiNi_(0.7)Co_(0.15)Mn_(0.15)O_(2)cathode(areal-mass-loading=39 mg cm~(-2))and a graphite anode(negative(N)/positive(P)capacity ratio=1.1)in order to fabricate an SSB full cell with bi-cell configuration.Under this constrained cell condition,the SSB full cell exhibits high volumetric energy density(480 Wh L_(cell)~(-1))and stable cyclability at 25℃,far exceeding the values reported by previous CSE-based SSBs.
文摘We investigate the p-Laplace heat equation ut-△_(p)u=ζ(t)f(u)in a bounded smooth domain.Using differential-inequality arguments,we prove blow-up results under suitable conditions onζ,f,and the initial datum u_(0).We also give an upper bound for the blow-up time in each case.
基金NSFC(Nos.11811145,12071364)the Fundamental Research Funds for the Central Universities(WUT:2020IA003)Key Scientific Research Foundation of the Higher Education Institutions of Henan Province,China(No.19A110004)。
文摘We investigate the initial boundary value problem of some semilinear pseudo-parabolic equations with Newtonian nonlocal term.We establish a lower bound for the blow-up time if blow-up does occur.Also both the upper bound for T and blow up rate of the solution are given when J(u 0)<0.Moreover,we establish the blow up result for arbitrary initial energy and the upper bound for T.As a product,we refine the lifespan when J(u 0)<0.
基金the National Natural Science Foundation of China(11771314)the Sichuan Science and Technology Program(2022JDTD0019)the Guizhou Province Science and Technology Basic Project(Qian Ke He Basic[2020]1Y011)。
文摘We consider the blow-up solutions to the following coupled nonlinear Schr¨odinger equations{iu_(t)+Δu+(|u|^(2p)+|u|^(p−1)|v|^(p+1))u=0,iv_(t)+Δv+(|v|^(2p)+|v|^(p−1)|u|^(p+1))v=0,u(0,x)=u0(x),v(0,x)=v0(x),x 2 R N,t0.On the basis of the conservation of mass and energy,we establish two sufficient conditions to obtain the existence of a blow-up for radially symmetric solutions.These results improve the blow-up result of Li and Wu[10]by dropping the hypothesis of finite variance((|x|u_(0),|x|v_(0))∈ L^(2)(R^(N))×L^(2)(R^(N))).
基金supported by the Beijing Natural Science Foundation(1212003)。
文摘Let?denote a smooth,bounded domain in R^(N)(N≥2).Suppose that g is a nondecreasing C^(1)positive function and assume that b(x)is continuous and nonnegative inΩ,and that it may be singular on■Ω.In this paper,we provide sufficient and necessary conditions on the existence of boundary blow-up solutions to the p-Laplacian problem△_(p)u=b(x)g(u)for x∈Ω,u(x)→+∞as dist(x,■Ω)→0.The estimates of such solutions are also investigated.Moreover,when b has strong singularity,the nonexistence of boundary blow-up(radial)solutions and infinitely many radial solutions are also considered.
