Blow Up for Reaction Diffusion Equations Under Dynamical Boundary Conditions
Blow Up for Reaction Diffusion Equations Under Dynamical Boundary Conditions
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DOI：
10.1081/pde-120019380
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发表时间：
2003-01
影响因子：
1.5
通讯作者：
J. Below;Gaëlle Pincet Mailly
中科院分区：
文献类型：
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作者：
J. Below;Gaëlle Pincet Mailly
对一类具有耗散动力学时间侧边条件的有界区域上的反应扩散方程，通过解的比较、能量方法和谱方法，证明了爆破现象的存在性。此外，不同的边界条件的爆破时间的依赖关系进行了研究，其中的动力学边界条件插值之间的Neumann边界条件和一定的Dirichlet边界条件的初始条件。这里提出的一些技术也适用于某些具有退化主部的抛物方程。[2]献给赫尔穆特·考尔教授65岁生日。
Abstract For a class of reaction diffusion equations in a bounded domain under dissipative dynamical time lateral boundary conditions, the occurence of blow up phenomena is shown by comparison of solutions, as well as by energy and spectral methods. Moreover, the dependence of the blow up time on different boundary conditions is investigated, where the dynamical boundary condition interpolates between the Neumann boundary condition and a certain Dirichlet boundary condition related to the initial condition. Some of the techniques presented here apply also to certain parabolic equations with degenerate principal part. †Dedicated to Professor Helmut Kaul on the occasion of his 65th birthday.