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Global and blow-up solutions for the nonlocal \(p\)-Laplacian evolution equation with weighted nonlinear nonlocal boundary condition. (English) Zbl 1295.35292

Summary: In this paper, we investigate global existence and blow-up properties of nonnegative solutions to a nonlocal \(p\)-Laplacian evolution equation with weighted nonlinear nonlocal boundary condition. By using the method of upper and lower solutions, we consider some effects of weight function and nonlinear exponent on the global and blow-up solutions. In addition, we show the blow-up rate estimate, blow-up profile and blow-up set for linear diffusion case.

MSC:

35K92 Quasilinear parabolic equations with \(p\)-Laplacian
35K65 Degenerate parabolic equations
35B33 Critical exponents in context of PDEs
35B40 Asymptotic behavior of solutions to PDEs
35K61 Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations
35B44 Blow-up in context of PDEs
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References:

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