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- W182498730 abstract "We survey recent results and present a number of open problems concerning the large-time behavior of solutions of semilinear parabolic equations with gradient nonlinearities. We focus on the model equation with a dissipative gradient term ut u = u p bjruj q ; where p, q > 1, b > 0, with homogeneous Dirichlet boundary conditions. Numerous papers were devoted to this equation in the last ten years, and we compare the results with those known for the case of the pure power reaction-diusion equation ( b = 0). In presence of the dissipative gradient term a number of new phenomena appear which do not occur when b = 0. The questions treated concern: sucient conditions for blowup, behavior of blowing up solutions, global existence and stability, unbounded global solutions, critical exponents, and stationary states." @default.
- W182498730 created "2016-06-24" @default.
- W182498730 creator A5001361123 @default.
- W182498730 date "2001-01-01" @default.
- W182498730 modified "2023-09-26" @default.
- W182498730 title "Recent results and open problems on parabolic equations with gradient nonlinearities." @default.
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