-convergence and homogenization of monotone damped hyperbolic equations.
Galerkin approximations for nonlinear evolution inclusions
In this paper we study the convergence properties of the Galerkin approximations to a nonlinear, nonautonomous evolution inclusion and use them to determine the structural properties of the solution set and establish the existence of periodic solutions. An example of a multivalued parabolic p.d.ei̇s also worked out in detail.
Galerkin method operator differential equations with Lipschitz continuous coefficients
Garding's inequality for elliptic differential operator with infinite number of variables.
General finite difference approximation to the Cauchy problem for nonlinear parabolic differential-functional equations
Generalized Backscattering and the Lax-Phillips Transform
2000 Mathematics Subject Classification: 35P25, 35R30, 58J50.Using the free-space translation representation (modified Radon transform) of Lax and Phillips in odd dimensions, it is shown that the generalized backscattering transform (so outgoing angle w = Sq in terms of the incoming angle with S orthogonal and Id-S invertible) may be further restricted to give an entire, globally Fredholm, operator on appropriate Sobolev spaces of potentials with compact support. As a corollary we show that the...
Generalized Cauchy problems for hyperbolic functional differential systems
A generalized Cauchy problem for hyperbolic functional differential systems is considered. The initial problem is transformed into a system of functional integral equations. The existence of solutions of this system is proved by using the method of successive approximations. Differentiability of solutions with respect to initial functions is proved. It is important that functional differential systems considered in this paper do not satisfy the Volterra condition.
Generalized dissipativeness in a Banach space.
Generalized Fractional Evolution Equation
2000 Mathematics Subject Classification: Primary 46F25, 26A33; Secondary: 46G20In this paper we study the generalized Riemann-Liouville (resp. Caputo) time fractional evolution equation in infinite dimensions. We show that the explicit solution is given as the convolution between the initial condition and a generalized function related to the Mittag-Leffler function. The fundamental solution corresponding to the Riemann-Liouville time fractional evolution equation does not admit a probabilistic...
Generalized gradients for locally Lipschitz integral functionals on non--type spaces of measurable functions
Let (Ω,μ) be a measure space, E be an arbitrary separable Banach space, be the dual equipped with the weak* topology, and g:Ω × E → ℝ be a Carathéodory function which is Lipschitz continuous on each ball of E for almost all s ∈ Ω. Put . Consider the integral functional G defined on some non--type Banach space X of measurable functions x: Ω → E. We present several general theorems on sufficient conditions under which any element γ ∈ X* of Clarke’s generalized gradient (multivalued C-subgradient)...
Generalized method of lines for first order partial functional differential equations
Classical solutions of initial boundary value problems are approximated by solutions of associated differential difference problems. A method of lines for an unknown function for the original problem and for its partial derivatives with respect to spatial variables is constructed. A complete convergence analysis for the method is given. A stability result is proved by using differential inequalities with nonlinear estimates of the Perron type for the given operators. A discretization...
Generalized random processes and Cauchy's problem for some partial differential systems.
Generalized Solution to a Semilinear Hyperbolic System with a Non-Lipshitz Nonlinearity.
Generalized solutions of mixed problems for quasilinear hyperbolic systems of functional partial differential equations in the Schauder canonic form
Generalized solutions to boundary value problems for quasilinear hyperbolic systems of partial differential-functional equations
Generalized solutions to quasilinear hyperbolic systems in the second canonical form are investigated. A theorem on existence, uniqueness and continuous dependence upon the boundary data is given. The proof is based on the methods due to L. Cesari and P. Bassanini for systems which are not functional.
Generation of Interface for an Allen-Cahn Equation with Nonlinear Diffusion
In this note, we consider a nonlinear diffusion equation with a bistable reaction term arising in population dynamics. Given a rather general initial data, we investigate its behavior for small times as the reaction coefficient tends to infinity: we prove a generation of interface property.
Generic solvability for the 3-D Navier-Stokes equations with nonregular force.
Geometric convergence of iterative methods for variational inequalities with -matrices and diagonal monotone operators
Geometrical interpretation of solutions of certain PDEs.
Global attractivity, oscillation and Hopf bifurcation for a class of diffusive hematopoiesis models
In this paper, we discuss the special diffusive hematopoiesis model with Neumann boundary condition. Sufficient conditions are provided for the global attractivity and oscillation of the equilibrium for Eq. (*), by using a new theorem we stated and proved. When P(t, χ) does not depend on a spatial variable χ ∈ Ω, these results are also true and extend or complement existing results. Finally, existence and stability of the Hopf bifurcation for Eq. (*) are studied.