Space-Time Regularity of Solutions of the Parabolic Stochastic Cauchy Problem

the problem of divine hiddenness

این رساله به مساله احتجاب الهی و مشکلات برهان مبتنی بر این مساله میپردازد. مساله احتجاب الهی مساله ای به قدمت ادیان است که به طور خاصی در مورد ادیان ابراهیمی اهمیت پیدا میکند. در ادیان ابراهیمی با توجه به تعالی خداوند و در عین حال خالقیت و حضور او و سخن گفتن و ارتباط شهودی او با بعضی از انسانهای ساکن زمین مساله ای پدید میاید با پرسشهایی از قبیل اینکه چرا ارتباط مستقیم ویا حداقل ارتباط وافی به ب...

Regularity of solutions to the parabolic fractional obstacle problem

In recent years, there has been an increasing interest in studying constrained variational problems with a fractional diffusion. One of the motivations comes from mathematical finance: jumpdiffusion processes where incorporated by Merton [14] into the theory of option evaluation to introduce discontinuous paths in the dynamics of the stock’s prices, in contrast with the classical lognormal diff...

Long time regularity of solutions of the Hele-Shaw problem

In this paper we study the long-time behavior of solutions of the one phase Hele-Shaw problem without surface tension. We show that after a finite time solutions of the Hele-Shaw problem become Lipschitz continuous with nondegenerate free boundary speed. It then follows that after a finite time the solution and the free boundary become smooth in space and time. 0 Introduction Let K = {x ∈ IR : ...

Regularity of weak solutions of the Cauchy problem to a fractional porous medium equation

This paper concerns the regularity of the weak solutions of the Cauchy problem to a fractional porous medium equation with a forcing term. In the recent work (Fan et al. in Comput. Math. Appl. 67:145-150, 2014), the authors established the existence of the weak solution and the uniqueness of the weak energy solution. In this paper, we show that the every nonnegative bounded weak energy solution...

Life Span of Positive Solutions for the Cauchy Problem for the Parabolic Equations