Abstract
We consider the Cauchy problem to a class of fast-diffusion non-Newtonian filtration equations. Besides the usual degeneracy in the fast-diffusion non-Newtonian filtration, the equation is degenerate or singular at infinity, depending on the sign of the parameter related to the coefficient of diffusion. Fujita type theorems are established and the critical Fujita exponent is determined. Specially, we also prove that the nontrivial solution blows up in a finite time on the critical situation.
Highlights
1 Introduction The purpose of this paper is to investigate the critical Fujita exponent for the following initial value problem:
There has been a lot of work on the critical Fujita exponents for various non
We study the problem ( ), ( ) and formulate the critical Fujita exponent as pc = q + (q + + μ )/(n + μ )
Summary
The purpose of this paper is to investigate the critical Fujita exponent for the following initial value problem:. Inspired by [ , , ], to prove the solutions’ blow-up, we analyze the interaction between the nonlinear source and nonlinear diffusion via precise estimates through constructing energy functions by use of the normalized principal eigenfunction of – in the unit ball B of Rn with homogeneous initial-boundary condition, rather than constructing subsolutions as the author did in [ , ] This method for equation ( ) and its special case ( ) basically depends upon the nonincreasing properties in the spatial variant of solutions, which is trivial with μ = μ , while it may be invalid if μ < μ.
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