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Critical nonlinearities in partial differential equations. (English) Zbl 1205.35024
Summary: This paper focuses on the role of critical nonlinearities within the framework of global solvability of nonlinear PDE’s. In particular, we present some new approach to blow-up issues for nonlinear problems.

MSC:
35B33 Critical exponents in context of PDEs
35B40 Asymptotic behavior of solutions to PDEs
35B44 Blow-up in context of PDEs
35K55 Nonlinear parabolic equations
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