论文信息 - LIFE SPAN OF NONNEGATIVE SOLUTIONS TO CERTAIN QUASILINEAR PARABOLIC CAUCHY PROBLEMS

LIFE SPAN OF NONNEGATIVE SOLUTIONS TO CERTAIN QUASILINEAR PARABOLIC CAUCHY PROBLEMS

We consider the problem (x)ut u m = h(x,t)u 1+p , x 2 R N , t > 0, with nonnegative, nontrivial, continuous initial condition, u(x,0) = u0(x) 6 0, u0(x) 0, x 2 R N. An integral inequality is obtained that can be used to find an exponent pc such that this problem has no nontrivial global solution when p pc. This integral inequality may also be used to estimate the maximal T > 0 such that there is a solution for 0 t 0, by obtaining a bound of the form T C0 #.

Hendrik J. Kuiper | Hendrik Kuiper

[1] L. Véron,et al. Blow-up results for nonlinear hyperbolic inequalities , 2000 .

[2] Kantaro Hayakawa,et al. On Nonexistence of Global Solutions of Some Semilinear Parabolic Differential Equations , 1973 .

[3] Y. Qi. The critical exponents of parabolic equations and blow-up in Rn , 1998, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[4] R. Kersner,et al. Local and Global Solvability of a Class of Semilinear Parabolic Equations , 1987 .

[5] M. Kirane,et al. Criticality for Some Evolution Equations , 2001 .

[6] Hiroshi Tanaka,et al. On the growing up problem for semilinear heat equations , 1977 .

[7] F. Weissler. Existence and non-existence of global solutions for a semilinear heat equation , 1981 .

[8] H. Fujita. On the blowing up of solutions fo the Cauchy problem for u_t=Δu+u^ , 1966 .

[9] K. Hayakawa,et al. On nonexistence of global solutions of some semilinear parabolic equations , 1973 .