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On global existence and stationary solutions for two classes of semilinear parabolic problems. (English) Zbl 0794.35089
Two initial-boundary value problems are studied. They received considerable interest before. Their common feature is the competition between a blow-up term and a damping term. The author fills several gaps in previous studies of steady states, blow-up and global existence.

MSC:
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35J65 Nonlinear boundary value problems for linear elliptic equations
35B40 Asymptotic behavior of solutions to PDEs
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