ﻻ يوجد ملخص باللغة العربية
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 $q$.
The Cauchy problem for the Hardy-Henon parabolic equation is studied in the critical and subcritical regime in weighted Lebesgue spaces on the Euclidean space $mathbb{R}^d$. Well-posedness for singular initial data and existence of non-radial forward
We study the Cauchy problem for the semilinear heat equation with the singular potential, called the Hardy-Sobolev parabolic equation, in the energy space. The aim of this paper is to determine a necessary and sufficient condition on initial data bel
We consider time fractional parabolic equations in both divergence and non-divergence form when the leading coefficients $a^{ij}$ are measurable functions of $(t,x_1)$ except for $a^{11}$ which is a measurable function of either $t$ or $x_1$. We obta
In this paper, we establish several Liouville type theorems for entire solutions to fractional parabolic equations. We first obtain the key ingredients needed in the proof of Liouville theorems, such as narrow region principles and maximum principles
We develop a strategy making extensive use of tent spaces to study parabolic equa-tions with quadratic nonlinearities as for the Navier-Stokes system. We begin with a new proof of the well-known result of Koch and Tataru on the well-posedness of Navi