一类带非线性边界条件的拟线性抛物方程的第二初边值问题

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The Second Initial-Boundary Value Problem for a Quasilinear Prabolic Equations With Nonlinear Boundary Conditions

摘要: 利用先验估计的方法讨论具非线性第二边界条件的快扩散方程解的存在性、唯一性、稳定性和渐近性.主要结果是:1)存在唯的整体广义解,解连续依赖于初值;2)存在T₀,t<T₀时解是无穷次可微的正则解;3)当t充分大时,解一致收敛到零.
- 快扩散 /
- 拟线性 /
- 非线性边界条件 /
- 第二初边值问题
Abstract: With prior estimate method,the existence,uniqueness,stability and large time behavior of the solution of second initial-boundary value problem for a fast diffusion equation with nonlinear boundary conditions are investigated.The main results are:1) there exists only one global weak solution which continuously depends on initial value; 2) when t<T₀,the solution is infinitely continuously differentiable and is a classical solution; 3) the solution converges to zero uniformly as t is large enough.
- fast-diffusion /
- quasilinear /
- nonlinear boundary conditions /
- second initial-boundary value problem

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