SOLVING A NONLINEAR PSEUDO-DIFFERENTIAL EQUATION OF BURGERS TYPE

2008 ◽  
Vol 08 (04) ◽  
pp. 613-624 ◽  
Author(s):  
NIELS JACOB ◽  
ALEXANDER POTRYKUS ◽  
JIANG-LUN WU
Keyword(s):  
Differential Equation ◽  
Differential Operator ◽  
Nonlinear Equations ◽  
Initial Value Problem ◽  
Symbolic Calculus ◽  
Pseudo Differential Operator ◽  
Initial Value ◽  
Semigroup Approach ◽  
Pseudo Differential Equation ◽  
Point Argument

In this paper, we study the initial value problem for a class of nonlinear equations of Burgers type in the following form: [Formula: see text] for u:(t,x) ∈ (0,∞) × ℝn ↦ ℝ, where q(x,D) is a pseudo-differential operator with negative definite symbol. We solve the initial value problem for the equation on ℝn by utilising a fix point argument based upon a combination of semigroup approach and Hoh's symbolic calculus.

On a nonlinear stochastic pseudo-differential equation driven by fractional noise

2017 ◽  
Vol 18 (01) ◽  
pp. 1850002 ◽  
Author(s):  
Junfeng Liu ◽  
Litan Yan
Keyword(s):  
Differential Equation ◽  
Differential Operator ◽  
Mild Solution ◽  
Malliavin Calculus ◽  
Measurable Function ◽  
Transition Density ◽  
Variable Order ◽  
Pseudo Differential Operator ◽  
Fractional Noise ◽  
Pseudo Differential Equation

In this paper, we study the existence, uniqueness and Hölder regularity of the solution to a class of nonlinear stochastic pseudo-differential equation of the following form [Formula: see text] where [Formula: see text] is a pseudo-differential operator with negative definite symbol of variable order which generates a stable-like process with transition density, the coefficient [Formula: see text] is a measurable function, and [Formula: see text] is a double-parameter fractional noise. In addition, the existence and Gaussian type estimates for the density of the mild solution are proved via Malliavin calculus.

THE INITIAL VALUE PROBLEM FOR THE DEEP BÉNARD CONVECTION EQUATIONS WITH DATA IN Lq

1996 ◽  
Vol 06 (02) ◽  
pp. 269-277 ◽  
Author(s):  
Z. CHARKI
Keyword(s):  
Fixed Point ◽  
Initial Value Problem ◽  
Existence And Uniqueness ◽  
Initial Value ◽  
Uniqueness Of Solutions ◽  
Bénard Convection ◽  
Benard Convection ◽  
Point Argument

A fixed point argument is used to prove the existence and uniqueness of solutions for the unsteady deep Bénard convection equations in [Formula: see text] for [Formula: see text].

scholarly journals Theory of differential offset continuation

Geophysics ◽  
2003 ◽  
Vol 68 (2) ◽  
pp. 718-732 ◽  
Author(s):  
Sergey Fomel
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Frequency Domain ◽  
Initial Value Problem ◽  
Data Transformation ◽  
Initial Value ◽  
Partial Differential ◽  
Reflection Data ◽  
Zero Offset

I introduce a partial differential equation to describe the process of prestack reflection data transformation in the offset, midpoint, and time coordinates. The equation is proved theoretically to provide correct kinematics and amplitudes on the transformed constant‐offset sections. Solving an initial‐value problem with the proposed equation leads to integral and frequency‐domain offset continuation operators, which reduce to the known forms of dip moveout operators in the case of continuation to zero offset.

Operational method for solving multi-term fractional differential equations with the generalized fractional derivatives

2014 ◽  
Vol 17 (1) ◽  
Author(s):  
Myong-Ha Kim ◽  
Guk-Chol Ri ◽  
Hyong-Chol O
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equations ◽  
Initial Value Problem ◽  
Fractional Derivatives ◽  
Operational Calculus ◽  
Operational Method ◽  
Initial Value ◽  
Constant Coefficients ◽  
Generalized Fractional Derivatives ◽  
Fractional Differential

AbstractThis paper provides results on the existence and representation of solution to an initial value problem for the general multi-term linear fractional differential equation with generalized Riemann-Liouville fractional derivatives and constant coefficients by using operational calculus of Mikusinski’s type. We prove that the initial value problem has the solution if and only if some initial values are zero.

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