On the equations $u_t + \nabla \cdot F\left( u \right) + 0$ and $u_t + \nabla \cdot F\left( u \right) = \nu \Delta u^1$
نویسندگان
چکیده
منابع مشابه
The Delta - Nabla Calculus of Variations
The discrete-time, the quantum, and the continuous calculus of variations have been recently unified and extended. Two approaches are followed in the literature: one dealing with minimization of delta integrals; the other dealing with minimization of nabla integrals. Here we propose a more general approach to the calculus of variations on time scales that allows to obtain both delta and nabla r...
متن کاملNabla discrete fractional calculus and nabla inequalities
Here we define a Caputo like discrete nabla fractional difference and we produce discrete nabla fractional Taylor formulae for the first time. We estimate their remaiders. Then we derive related discrete nabla fractional Opial, Ostrowski, Poincaré and Sobolev type inequalities .
متن کاملHenstock–Kurzweil delta and nabla integrals
We will study the Henstock–Kurzweil delta and nabla integrals, which generalize the Henstock–Kurzweil integral. Many properties of these integrals will be obtained. These results will enable time scale researchers to study more general dynamic equations. The Hensock–Kurzweil delta (nabla) integral contains the Riemann delta (nabla) and Lebesque delta (nabla) integrals as special cases.
متن کاملA Stacked Delta-Nabla Self-Adjoint Problem of Even Order
Existence criteria for two positive solutions to a nonlinear, even-order stacked deltanabla boundary value problem with stacked, vanishing conditions at the two endpoints are found using the method of Green’s functions. A few examples are given for standard time scales. The corresponding even-order nabla-delta problem is also discussed in detail. c © 2003 Elsevier Science Ltd. All rights reserv...
متن کاملPositive solutions for asymptotically periodic Kirchhoff-type equations with critical growth
In this paper, we consider the following Kirchhoff-type equations: $-left(a+bint_{mathbb{R}^{3}}|nabla u|^{2}right)Delta u+V(x) u=lambda$ $f(x,u)+u^{5}, quad mbox{in }mathbb{R}^{3},$ $u(x)>0, quad mbox{in }mathbb{R}^{3},$ $uin H^{1}(mathbb{R}^{3}) ,$ where $a,b>0$ are constants and $lambda$ is a positive parameter. The aim of this paper is to study the existence of positive ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1969
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1969-12423-7