论文标题
在非线性Miyadera-Voigt扰动上
On nonlinear Miyadera-Voigt perturbations
论文作者
论文摘要
令$ a，c，p：d（a）\ subset x \ to x $是banach space $ x $上的线性运算符，以便$ -a -a $在$ x $上产生强烈连续的semigroup，而$ f：x \ to x $是全球lipschitz的功能。我们研究了$ \ dot {u}（t）= g（u（t））$的半线性方程式的适合性，其中$ g：d（a）\ x $是由$ g = -a+c+c+f \ f \ circ p $定义的非线性图。实际上，使用最大$ l^p $的概念和固定点定理，我们确定了上述半线性方程的强大解决方案的存在和唯一性。我们通过应用于Dirichlet和Neumann边界条件的非线性热方程以及非局部无界非边界非线性扰动来说明我们的结果。
Let $A,C,P:D(A)\subset X\to X$ be linear operators on a Banach space $X$ such that $-A$ generates a strongly continuous semigroup on $X$, and $F:X\to X$ be a globally Lipschitz function. We study the well-posedness of semilinear equations of the form $\dot{u}(t)=G(u(t))$, where $G:D(A)\to X$ is a nonlinear map defined by $G=-A+C+F\circ P$. In fact, using the concept of maximal $L^p$-regularity and a fixed point theorem, we establish the existence and uniqueness of a strong solution for the above-mentioned semilinear equation. We illustrate our results by applications to nonlinear heat equations with respect to Dirichlet and Neumann boundary conditions, and a nonlocal unbounded nonlinear perturbation.
