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Zeitschrift für Analysis und ihre Anwendungen


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Volume 15, Issue 4, 1996, pp. 917–933
DOI: 10.4171/ZAA/737

Published online: 1996-12-31

On a Class of Nonlinear Neumann Problems of Parabolic Type: Blow-Up of Solutions

M.A. Pozio[1] and Alberto Tesei[2]

(1) Università di Roma La Sapienza, Italy
(2) Università di Roma La Sapienza, Italy

We investigate large time behaviour of solutions for a class of nonlinear Neumann parabolic problems of indefinite type, possibly degenerate. Depending on the features of the problem, several parameters play a role to establish global boundedness or finite time blow-up of solutions. The occurrence of either situation is related with the existence of stationary solutions. Proofs make extensive use of monotonicity methods.

Keywords: Nonlinear Neumann parabolic equations, reaction terms of indefinite type, blow-up of solutions, existence and non-existence of stationary solutions

Pozio M.A., Tesei Alberto: On a Class of Nonlinear Neumann Problems of Parabolic Type: Blow-Up of Solutions. Z. Anal. Anwend. 15 (1996), 917-933. doi: 10.4171/ZAA/737