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Global and blow-up solutions for nonlinear parabolic equations with a gradient term. (English) Zbl 1243.35028

Authors’ abstract: “This paper studies a Neumann initial-boundary value problem for a nonlinear parabolic equation with a gradient term in a bounded domain in the \(N\)-dimensional Euclidean space with \(N\geq2\) and a smooth boundary. By using upper and lower solutions, existence of a global positive solution \(u\), an upper estimate of \(u\), blowup of \(u\), and an upper bound of the blow-up time are investigated. For illustrations, two examples are given.”

MSC:

35B44 Blow-up in context of PDEs
35K20 Initial-boundary value problems for second-order parabolic equations
35K55 Nonlinear parabolic equations
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