论文标题
非线性边界价值问题相对于一维热方程
Nonlinear boundary value problems relative to one dimensional heat equation
论文作者
论文摘要
我们考虑存在解决方案的问题$ u $至$ \ partial_t u- \ partial_ {xx} u = 0 $ in $（0，t）\ times \ times \ mathbb {r} _+$，均受边界条件$ -U_X（t，0）+g（t，0）$（t，t，0）$（u（t，0）$（us）$（$ nes $（0）$（0）$（0）$（0） $ g $连续的非递减功能。当$ p> 1 $时，我们研究了$ \ partial_t u- \ partial_ {xx} u = 0 $ in $ \ mathbb {r} _+\ times \ times \ times \ mathbb {r} _+$ in $ \ partial_ {xx} u = 0 $ = 0 $的自相似解决方案的集合。最后，我们向更高维度的框架提供了各种扩展。
We consider the problem of existence of a solution $u$ to $\partial_t u-\partial_{xx} u = 0$ in $(0,T)\times\mathbb{R}_+$ subject to the boundary condition $-u_x(t,0)+g(u(t,0))=μ$ on $(0,T)$ where $μ$ is a measure on $(0,T)$ and $g$ a continuous nondecreasing function. When $p>1$ we study the set of self-similar solutions of $\partial_t u-\partial_{xx} u = 0$ in $\mathbb{R}_+\times\mathbb{R}_+$ such that $-u_x(t,0)+u^p=0$ on $(0,\infty)$. At end, we present various extensions to a higher dimensional framework.
