In thispaper,theexistence oftravelling frontsolution fora classofcom petition-diffu- sion system w ith high-order singular point w it = diw ixx - w αii fi(w ),x ∈R,t> 0,i= 1,2 (Ⅰ) is studied,w here di,αi>...In thispaper,theexistence oftravelling frontsolution fora classofcom petition-diffu- sion system w ith high-order singular point w it = diw ixx - w αii fi(w ),x ∈R,t> 0,i= 1,2 (Ⅰ) is studied,w here di,αi> 0 (i= 1,2) and w = (w 1(x,t),w 2(x,t)).Under the certain assum ptions on f,itis show ed thatifαi< 1 for som e i,then (Ⅰ) has no travelling frontsolution,ifαi≥1 for i= 1,2,then there isa c0,c:c0≥c> 0,w herecis called the m inim alwavespeed of(Ⅰ),such thatifc≥c0 orc= c,then (Ⅰ) has a travelling frontsolution,ifc< c,then (Ⅰ) hasno travel- ling frontsolution by using the shooting m ethod in com bination w ith a com pactness argum ent.展开更多
The development of agricultural science and technology has been accelerating, which has promoted the scientific and modern development of agricultural planting. In addition, advanced technology can be adopted in plant...The development of agricultural science and technology has been accelerating, which has promoted the scientific and modern development of agricultural planting. In addition, advanced technology can be adopted in planting and maintenance to promote the realization of large-scale agricultural production and help farmers to create higher income. At present, Shandong has stepped up the construction of irrigation and water conservancy projects, the main purpose of which is to adjust water resources to meet the needs of crop growth, but there is still a serious waste of water resources. Shandong Province is internationally recognized as an "extremely water-deficient area", and the water demand for agricultural irrigation is large and waste is serious. Therefore, it is necessary to play the guiding role of the concept of energy conservation and emission reduction, and adopt efficient water-saving irrigation technology to create higher economic benefits and realize the efficient use of water resources. This paper focuses on the application of high-efficiency water-saving irrigation technology in farmland water conservancy projects.展开更多
This paper deals with the blow up properties of solutions to semilinear heat equation u t- Δ u=u p in R N +×(0,T) with the nonlinear boundary condition -ο u ο x 1 = u q for x 1=0,t∈(0,T) ....This paper deals with the blow up properties of solutions to semilinear heat equation u t- Δ u=u p in R N +×(0,T) with the nonlinear boundary condition -ο u ο x 1 = u q for x 1=0,t∈(0,T) .It has been proved that if max( p,q) ≤1,every nonnegative solution is global.When min (p,q) >1 by letting α=1p-1 and β=12(q-1) it follows that if max (α,β)≥N2 ,all nontrivial nonnegative solutions are nonglobal,whereas if max (α,β)<N2 ,there exist both global and nonglobal solutions.Moreover,the exact blow up rates are established.展开更多
This paper deals with the blow-up properties of solutions to the systems ut=Δu,vt=Δv in BR × (O,T) subject to nonlinear boundary conditions δu/δη=v^p,δu/δη=u^q, in SR×(O,T). It is shown that under ce...This paper deals with the blow-up properties of solutions to the systems ut=Δu,vt=Δv in BR × (O,T) subject to nonlinear boundary conditions δu/δη=v^p,δu/δη=u^q, in SR×(O,T). It is shown that under certain conditions the solution blows up at a finite time and the blow-up only occurs on the boundary. The self-similar solution for the one-dimensional case has been studied. Moreover, the exact blow-up rates are also derived.展开更多
文摘In thispaper,theexistence oftravelling frontsolution fora classofcom petition-diffu- sion system w ith high-order singular point w it = diw ixx - w αii fi(w ),x ∈R,t> 0,i= 1,2 (Ⅰ) is studied,w here di,αi> 0 (i= 1,2) and w = (w 1(x,t),w 2(x,t)).Under the certain assum ptions on f,itis show ed thatifαi< 1 for som e i,then (Ⅰ) has no travelling frontsolution,ifαi≥1 for i= 1,2,then there isa c0,c:c0≥c> 0,w herecis called the m inim alwavespeed of(Ⅰ),such thatifc≥c0 orc= c,then (Ⅰ) has a travelling frontsolution,ifc< c,then (Ⅰ) hasno travel- ling frontsolution by using the shooting m ethod in com bination w ith a com pactness argum ent.
文摘The development of agricultural science and technology has been accelerating, which has promoted the scientific and modern development of agricultural planting. In addition, advanced technology can be adopted in planting and maintenance to promote the realization of large-scale agricultural production and help farmers to create higher income. At present, Shandong has stepped up the construction of irrigation and water conservancy projects, the main purpose of which is to adjust water resources to meet the needs of crop growth, but there is still a serious waste of water resources. Shandong Province is internationally recognized as an "extremely water-deficient area", and the water demand for agricultural irrigation is large and waste is serious. Therefore, it is necessary to play the guiding role of the concept of energy conservation and emission reduction, and adopt efficient water-saving irrigation technology to create higher economic benefits and realize the efficient use of water resources. This paper focuses on the application of high-efficiency water-saving irrigation technology in farmland water conservancy projects.
文摘This paper deals with the blow up properties of solutions to semilinear heat equation u t- Δ u=u p in R N +×(0,T) with the nonlinear boundary condition -ο u ο x 1 = u q for x 1=0,t∈(0,T) .It has been proved that if max( p,q) ≤1,every nonnegative solution is global.When min (p,q) >1 by letting α=1p-1 and β=12(q-1) it follows that if max (α,β)≥N2 ,all nontrivial nonnegative solutions are nonglobal,whereas if max (α,β)<N2 ,there exist both global and nonglobal solutions.Moreover,the exact blow up rates are established.
文摘This paper deals with the blow-up properties of solutions to the systems ut=Δu,vt=Δv in BR × (O,T) subject to nonlinear boundary conditions δu/δη=v^p,δu/δη=u^q, in SR×(O,T). It is shown that under certain conditions the solution blows up at a finite time and the blow-up only occurs on the boundary. The self-similar solution for the one-dimensional case has been studied. Moreover, the exact blow-up rates are also derived.
