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Conserved quantities and generalized solutions of the ultradiscrete KdV equation
Conserved quantities generalized solutions ultradiscrete KdV equation
2011/2/22
We construct generalized solutions to the ultradiscrete KdV equation,including the so-called negative solition solutions. The method is based on the ultradiscretization of soliton solutions to the dis...
Global generalized solutions for Maxwell-alpha and Euler-alpha equations
Global generalized solutions Maxwell-alpha Euler-alpha equations
2011/2/24
We study initial-boundary value problems for the Lagrangian averaged alpha models for the equations of motion for the corotational Maxwell and inviscid fluids in 2D and 3D. We show existence of (globa...
On completeness of elementary generalized solutions of a class of operator-differential equations of a higher order
Hilbert space existence of generalized solution operator-differential equation
2010/2/25
In this paper we give definition of m-fold completeness and prove a theorem on completeness of elementary generalized solution of corresponding boundary value problems at which the equation describes ...
THE GENERALIZED SOLUTIONS OF PBVP FORINTEGRO-DIFFERENTIAL EQUATIONS
Integro-differential equations periodic
2007/8/7
In this paper, we study the periodic boundary value problems for a class ofnonlinear integro-differential equations of Volterra type with Caratheodory condition. Weobtain an existence result of genera...
Generalized Solutions of a Class of Linear and Quasi-Linear Degenerated Hyperbolic Equations
Linear Quasi-Linear Degenerated Hyperbolic Equations
2010/3/3
The equation L(u):=k(y)uxx-\partialy(\ell(y)uy)+r(x,y)u=f(x,y,u), where k(y)>0, \ell(y)>0 for y>0,k(0)=\ell(0)=0 and limy\rightarrow 0k(y)/\ell(y) exists, is strictly hyperbolic for y>0 and its order ...