In this paper, the initial boundary value problem of semilinear degenerate reaction-diffusion systems is studied. The regularization method and upper and lower solutions technique are employed to show the existence an...In this paper, the initial boundary value problem of semilinear degenerate reaction-diffusion systems is studied. The regularization method and upper and lower solutions technique are employed to show the existence and continuation of a positive classical solution. The location of quenching points is found. The critical length is estimated by the eigenvalue method.展开更多
In this paper, blow-up estimates for a class of quasiliuear reaction-diffusion equations(non-Newtonian filtration equations) in term of the nouexistence result for quasilinear ordinary differential equations are estab...In this paper, blow-up estimates for a class of quasiliuear reaction-diffusion equations(non-Newtonian filtration equations) in term of the nouexistence result for quasilinear ordinary differential equations are established to extends the result for semi-linear reaction-diffusion equations(Newtonian filtration equations).展开更多
The authors study radial solutions to a model equation for the Navier-Stokes equations. It is shown that the model equation has self-similar singular solution if 5 ≤ n ≤ 9. It is also shown that the solution will bl...The authors study radial solutions to a model equation for the Navier-Stokes equations. It is shown that the model equation has self-similar singular solution if 5 ≤ n ≤ 9. It is also shown that the solution will blow up if the initial data is radial, large enough and n ≥ 5.展开更多
文摘In this paper, the initial boundary value problem of semilinear degenerate reaction-diffusion systems is studied. The regularization method and upper and lower solutions technique are employed to show the existence and continuation of a positive classical solution. The location of quenching points is found. The critical length is estimated by the eigenvalue method.
基金Supported by the National Natural Science Foundation of China(10172011)
文摘In this paper, blow-up estimates for a class of quasiliuear reaction-diffusion equations(non-Newtonian filtration equations) in term of the nouexistence result for quasilinear ordinary differential equations are established to extends the result for semi-linear reaction-diffusion equations(Newtonian filtration equations).
基金supported by the China Postdoctoral Science Foundation (No. 20070410683).
文摘The authors study radial solutions to a model equation for the Navier-Stokes equations. It is shown that the model equation has self-similar singular solution if 5 ≤ n ≤ 9. It is also shown that the solution will blow up if the initial data is radial, large enough and n ≥ 5.
