论文标题
从边界测量中恢复反应扩散方程的非线性项
Recovery of nonlinear terms for reaction diffusion equations from boundary measurements
论文作者
论文摘要
我们考虑确定在非线性抛物线方程中出现的一般半线性术语的逆问题。为此，我们得出了一个新标准，该标准允许从方程式的横向边界测量值中证明某些一般类别的半线性项的全局恢复，其初始条件固定为零。更准确地说，我们证明了这似乎是第一次，这是根据时间和空间变量的独特而稳定的恢复，这是从与抛物线dirichlet到neumann映射的知识相关的非线性方程式的解决方案的独立性，独立的，与与初始条件的方程式相关的抛物线dirichlet dirichlet to-neumann图的知识。我们的方法基于所考虑的反问题的第二个线性化。
We consider the inverse problem of determining a general semilinear term appearing in nonlinear parabolic equations. For this purpose, we derive a new criterion that allows to prove global recovery of some general class of semilinear terms from lateral boundary measurements of solutions of the equation with initial condition fixed at zero. More precisely, we prove, for what seems to be the first time, the unique and stable recovery of general semilinear terms depending on time and space variables independently of the solution of the nonlinear equation from the knowledge of the parabolic Dirichlet-to-Neumann map associated with the solution of the equation with initial condition fixed at zero. Our approach is based on the second linearization of the inverse problem under consideration.
