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Nonexistence of positive solutions to a quasilinear elliptic system and blow-up estimates for a non-Newtonian filtration system. (English) Zbl 1050.35035

For the following reaction-diffusion systems
\[ u_t=\text{div} (| Du| ^{p-2}Du)+v^\alpha,\quad v_t=\text{div} (| Dv| ^{q-2}Dv)+w^\beta,\quad w_t=\text{div} (| Dw| ^{m-2}Dw)+u^\gamma \]
on a ball the authors find conditions, in terms of the constants \(p,q,m,\alpha,\beta,\gamma\) and the dimension of the ball, which imply that the above systems do not admit positive and radially symmetric stationary solutions. They have also obtained blow-up result for the nonnegative, radially symmetric and decreasing solutions of the above systems.

MSC:

35K50 Systems of parabolic equations, boundary value problems (MSC2000)
35K55 Nonlinear parabolic equations
35K57 Reaction-diffusion equations
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References:

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