Application of capacities to space–time fractional dissipative equations I: regularity and the blow-up set

Blow up Results for Fractional Differential Equations and Systems

Boundary blow up solutions for fractional elliptic equations

In this article we study existence of boundary blow up solutions for some fractional elliptic equations including (−∆)u+ u = f in Ω, u = g on Ω, lim x∈Ω,x→∂Ω u(x) = ∞, where Ω is a bounded domain of class C2, α ∈ (0, 1) and the functions f : Ω → R and g : RN \ Ω̄ → R are continuous. We obtain existence of a solution u when the boundary value g blows up at the boundary and we get explosion rate f...

Regularity and Blow up for Active Scalars

We review some recent results for a class of fluid mechanics equations called active scalars, with fractional dissipation. Our main examples are the surface quasigeostrophic equation, the Burgers equation, and the Cordoba-Cordoba-Fontelos model. We discuss nonlocal maximum principle methods which allow to prove existence of global regular solutions for the critical dissipation. We also recall w...

Stability of the blow-up time and the blow-up set under perturbations

In this paper we prove a general result concerning continuity of the blow-up time and the blow-up set for an evolution problem under perturbations. This result is based on some convergence of the perturbations for times smaller than the blow-up time of the unperturbed problem together with uniform bounds on the blow-up rates of the perturbed problems. We also present several examples. Among the...

existence and approximate $l^{p}$ and continuous solution of nonlinear integral equations of the hammerstein and volterra types

بسیاری از پدیده ها در جهان ما اساساً غیرخطی هستند، و توسط معادلات غیرخطی ‎‏بیان شد‎‎‏ه اند. از آنجا که ظهور کامپیوترهای رقمی با عملکرد بالا، حل مسایل خطی را آسان تر می کند. با این حال، به طور کلی به دست آوردن جوابهای دقیق از مسایل غیرخطی دشوار است. روش عددی، به طور کلی محاسبه پیچیده مسایل غیرخطی را اداره می کند. با این حال، دادن نقاط به یک منحنی و به دست آوردن منحنی کامل که اغلب پرهزینه و ...