Existence of solutions for nonlinear parabolic problems

Nikolaos Halidias; Nikolaos S. Papageorgiou

Periodic problems and problems with discontinuities for nonlinear parabolic equations

Tiziana Cardinali, Nikolaos S. Papageorgiou (2000)

Czechoslovak Mathematical Journal

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In this paper we study nonlinear parabolic equations using the method of upper and lower solutions. Using truncation and penalization techniques and results from the theory of operators of monotone type, we prove the existence of a periodic solution between an upper and a lower solution. Then with some monotonicity conditions we prove the existence of extremal solutions in the order interval defined by an upper and a lower solution. Finally we consider problems with discontinuities and...

Transition from decay to blow-up in a parabolic system

Pavol Quittner (1998)

Archivum Mathematicum

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We show a locally uniform bound for global nonnegative solutions of the system $u_{t} = Δ u + u v - b u$ , $v_{t} = Δ v + a u$ in $(0, + \infty) \times Ω$ , $u = v = 0$ on $(0, + \infty) \times \partial Ω$ , where $a > 0$ , $b \geq 0$ and $Ω$ is a bounded domain in $ℝ^{n}$ , $n \leq 2$ . In particular, the trajectories starting on the boundary of the domain of attraction of the zero solution are global and bounded.

Displaying similar documents to “Existence of solutions for nonlinear parabolic problems”

Periodic problems and problems with discontinuities for nonlinear parabolic equations

Transition from decay to blow-up in a parabolic system