共查询到20条相似文献,搜索用时 328 毫秒
1.
Approximating the coefficients in semilinear stochastic partial differential equations 总被引:1,自引:0,他引:1
We investigate, in the setting of UMD Banach spaces E, the continuous dependence on the data A, F, G and ξ of mild solutions of semilinear stochastic evolution equations with multiplicative noise of the form
$ \left\{ {l} {\rm d}X(t) = [AX(t) + F(t, X(t))] \, {\rm d}t + G(t, X(t)) \, {\rm d}W_H(t),\quad t \in [0,T],\\ X(0) = \xi,
\right. $ \left\{ \begin{array}{l} {\rm d}X(t) = [AX(t) + F(t, X(t))] \, {\rm d}t + G(t, X(t)) \, {\rm d}W_H(t),\quad t \in [0,T],\\ X(0) = \xi, \end{array}
\right. 相似文献
2.
We consider the effect of perturbations of A on the solution to the following semi-linear parabolic stochastic partial differential equation: $$\left\{\begin{array}{ll}{\rm d}U(t) & = AU(t)\,{\rm d}t + F(t,U(t))\,{\rm d}t + G(t,U(t))\,{\rm d}W_H(t), \quad t > 0;\\U(0)& = x_0. \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad({\rm SDE})\end{array} \right.$$ Here, A is the generator of an analytic C 0-semigroup on a UMD Banach space X, H is a Hilbert space, W H is an H-cylindrical Brownian motion, ${G:[0,T]\times X\rightarrow \mathcal{L}(H, X_{\theta_G}^{A})}$ , and ${F : [0, T]\times X \rightarrow X_{\theta_F}^{A}}$ for some ${\theta_G > -\frac{1}{2}, \theta_F > -\frac{3}{2}+\frac{1}{\tau}}$ , where ${\tau\in [1, 2]}$ denotes the type of the Banach space and ${X_{\theta_F}^{A}}$ denotes the fractional domain space or extrapolation space corresponding to A. We assume F and G to satisfy certain global Lipschitz and linear growth conditions. Let A 0 denote the perturbed operator and U 0 the solution to (SDE) with A substituted by A 0. We provide estimates for ${\|U - U_0\|_{L^p(\Omega;C([0,T];X))}}$ in terms of ${D_{\delta}(A, A_0) := \|R(\lambda : A) - R(\lambda : A_0)\|_{\mathcal{L}(X^{A}_{\delta-1},X)}}$ . Here, ${\delta\in [0, 1]}$ is assumed to satisfy ${0\leq \delta < {\rm min}\{\frac{3}{2} - \frac{1}{\tau} + \theta_F,\, \frac{1}{2} - \frac{1}{p} + \theta_G \}}$ . The work is inspired by the desire to prove convergence of space approximations of (SDE). In this article, we prove convergence rates for the case that A is approximated by its Yosida approximation. 相似文献
3.
Tommaso Leonori Francesco Petitta 《Calculus of Variations and Partial Differential Equations》2011,42(1-2):153-187
In this paper we deal with local estimates for parabolic problems in ${\mathbb{R}^N}$ with absorbing first order terms, whose model is $$\left\{\begin{array}{l@{\quad}l}u_t- \Delta u +u |\nabla u|^q = f(t,x) \quad &{\rm in}\, (0,T) \times \mathbb{R}^N\,,\\u(0,x)= u_0 (x) &{\rm in}\, \mathbb{R}^N \,,\quad\end{array}\right.$$ where ${T >0 , \, N\geq 2,\, 1 < q \leq 2,\, f(t,x)\in L^1\left( 0,T; L^1_{\rm loc} \left(\mathbb{R}^N\right)\right)}$ and ${u_0\in L^1_{\rm loc}\left(\mathbb{R}^{N}\right)}$ . 相似文献
4.
Y. Guo 《Ukrainian Mathematical Journal》2011,62(9):1409-1419
We consider the existence of nontrivial solutions of the boundary-value problems for nonlinear fractional differential equations
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