ترغب بنشر مسار تعليمي؟ اضغط هنا

An alternative proof of well-posedness of stochastic evolution equations in the variational setting

79   0   0.0 ( 0 )
 نشر من قبل Carlo Marinelli
 تاريخ النشر 2020
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

We present a new proof of well-posedness of stochastic evolution equations in variational form, relying solely on a (nonlinear) infinite-dimensional approximation procedure rather than on classical finite-dimensional projection arguments of Galerkin type.



قيم البحث

اقرأ أيضاً

We study the Hardy-Henon parabolic equations on $mathbb{R}^{N}$ ($N=2, 3$) under the effect of an additive fractional Brownian noise with Hurst parameter $H>maxleft(1/2, N/4right).$ We show local existence and uniqueness of a mid $L^{q}$-solution under suitable assumptions on $q$.
74 - Carlo Marinelli 2019
We prove a maximum principle for mild solutions to stochastic evolution equations with (locally) Lipschitz coefficients and Wiener noise on weighted $L^2$ spaces. As an application, we provide sufficient conditions for the positivity of forward rates in the Heath-Jarrow-Morton model, considering the associated Musiela SPDE on a homogeneous weighted Sobolev space.
107 - Zhaoyang Qiu , Huaqiao Wang 2021
We consider the stochastic electrokinetic flow in a smooth bounded domain $mathcal{D}$, modelled by a Nernst-Planck-Navier-Stokes system with a blocking boundary conditions for ionic species concentrations, perturbed by multiplicative noise. Several results are established in this paper. In both $2d$ and $3d$ cases, we establish the global existence of weak martingale solution which is weak in both PDEs and probability sense, and also the existence and uniqueness of the maximal strong pathwise solution which is strong in PDEs and probability sense. Particularly, we show that the maximal pathwise solution is global one in $2d$ case without the restriction of smallness of initial data.
We provide sufficient conditions on the coefficients of a stochastic evolution equation on a Hilbert space of functions driven by a cylindrical Wiener process ensuring that its mild solution is positive if the initial datum is positive. As an applica tion, we discuss the positivity of forward rates in the Heath-Jarrow-Morton model via Musielas stochastic PDE.
In this paper, we discuss the well-posedness of the Cauchy problem associated with the third-order evolution equation in time $$ u_{ttt} +A u + eta A^{frac13} u_{tt} +eta A^{frac23} u_t=f(u) $$ where $eta>0$, $X$ is a separable Hilbert space, $A:D(A) subset Xto X$ is an unbounded sectorial operator with compact resolvent, and for some $lambda_0>0$ we have $mbox{Re}sigma(A)>lambda_0$ and $f:D(A^{frac13})subset Xto X$ is a nonlinear function with suitable conditions of growth and regularity.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا