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On the asymptotic behaviour of solutions of some nonlinear elliptic and parabolic equations

✍ Scribed by Ramón Quintanilla

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
166 KB
Volume
52
Category
Article
ISSN
0362-546X

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✦ Synopsis

In this paper, we investigate the spatial asymptotic behaviour of some nonlinear elliptic and parabolic equations related with the process of di usion-convection. We obtain results of the kind of the Phragmà en-Lindelof alternative. The main idea of the paper is to obtain a nonlinear ordinary di erential inequality which is satisÿed by a certain measure of the solutions. This ordinary inequality was studied by Horgan and Payne in a recent paper. We obtain our results with the help of estimates known for this inequality. When the solutions tend to zero, we also obtain an estimate for the amplitude term.

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On solutions of some nonlinear degenerat
On solutions of some nonlinear degenerate parabolic equations
✍ Tokumori Nanbu 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 350 KB

We study the existence and some estimates of solution of the initial- boundary value problem for some nonlinear degenerate parabolic equations \[ u_{t}=\Delta\left(|u|^{m-1} u\right)+\sum_{k=1}^{N} b_{k} \frac{\partial\left(|u|^{l} u\right)}{\partial x_{k}}-A(u)+f(x, t) \]