ترغب بنشر مسار تعليمي؟ اضغط هنا

On the asimptotic behavior of solutions of the Cauchy problem for parabolic equations with time periodic coefficients

134   0   0.0 ( 0 )
 نشر من قبل Nicolai Krylov
 تاريخ النشر 2021
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

We are considering the asimptotic behavior as $ttoinfty$ of solutions of the Cauchy problem for parabolic second order equations with time periodic coefficients. The problem is reduced to considering degenerate time-homogeneous diffusion processes on the product of a unit circle and Euclidean space.

قيم البحث

اقرأ أيضاً

We study asymptotic behavior in a class of non-autonomous second order parabolic equations with time periodic unbounded coefficients in $mathbb Rtimes mathbb R^d$. Our results generalize and improve asymptotic behavior results for Markov semigroups h aving an invariant measure. We also study spectral properties of the realization of the parabolic operator $umapsto {cal A}(t) u - u_t$ in suitable $L^p$ spaces.
389 - Anatoly N. Kochubei 2013
We consider an evolution equation with the Caputo-Dzhrbashyan fractional derivative of order $alpha in (1,2)$ with respect to the time variable, and the second order uniformly elliptic operator with variable coefficients acting in spatial variables. This equation describes the propagation of stress pulses in a viscoelastic medium. Its properties are intermediate between those of parabolic and hyperbolic equations. In this paper, we construct and investigate a fundamental solution of the Cauchy problem, prove existence and uniqueness theorems for such equations.
We consider Cauchy problem for a divergence form second order parabolic operator with rapidly oscillating coefficients that are periodic in spatial variable and random stationary ergodic in time. As was proved in [25] and [13] in this case the homoge nized operator is deterministic. We obtain the leading terms of the asymptotic expansion of the solution , these terms being deterministic functions, and show that a properly renormalized difference between the solution and the said leading terms converges to a solution of some SPDE.
113 - Shanjian Tang , Wenning Wei 2013
This paper is concerned with solution in H{o}lder spaces of the Cauchy problem for linear and semi-linear backward stochastic partial differential equations (BSPDEs) of super-parabolic type. The pair of unknown variables are viewed as deterministic s patial functionals which take values in Banach spaces of random (vector) processes. We define suitable functional H{o}lder spaces for them and give some inequalities among these H{o}lder norms. The existence, uniqueness as well as the regularity of solutions are proved for BSPDEs, which contain new assertions even on deterministic PDEs.
99 - Janna Lierl 2017
We introduce a notion of quasilinear parabolic equations over metric measure spaces. Under sharp structural conditions, we prove that local weak solutions are locally bounded and satisfy the parabolic Harnack inequality. Applications include the para bolic maximum principle and pointwise estimates for weak solutions.
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