linear abstract Cauchy problem
Abstract differential inequalities and the Cauchy problem for infinite dimensional linear functional differential equations
... the Cauchy problem for general functional dif- ferential equations, the most powerful and e ffi cient one being based on the use of dif- ferential inequalities and developed most extensively for ordinary ...
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On efficient abstract method for the study of Cauchy problem for a second order differential equation set on a singular cylindrical domain
... (2.11) Lemma 2.2. The densely closed linear operator (A, D(A)) defined by (2.7) is a sectorial operator with µ = 0 and δ = π 2 . Proof. See section 3.1.1 in [16], in where a complete study of more general elliptic ...
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DEGENERATE DISTRIBUTED CONTROL SYSTEMS WITH FRACTIONAL TIME DERIVATIVE
... the Cauchy problem to the nondegenerate fractional differential equation ( X = Y , L = I in ...value problem to the degenerate fractional differential ...conditions. Abstract results are ...
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Nonlocal impulsive fractional semilinear differential equations with almost sectorial operators
... of abstract fractional cauchy problems using almost sectorial operators and in [32], ...for cauchy problem for non-autonomous evolution equation, in which the operator in the linear ...
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On the Cauchy problem for a linear harmonic oscillator with pure delay
... the problem discussion and writing the introduction ...the abstract well-posedness for the harmonic oscillator with pure delay and studied its asymptotics as the delay parameter goes to ...
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Algorithm for solving the Cauchy problem for stationary systems of fractional order linear ordinary differential equations
... the Cauchy problem for a homogeneous system of fractional order linear differential equations with constant coefficients ...the Cauchy problem with high ...
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Numerical Results of Sub Cauchy Problem for Linear Elasticity
... sub-Cauchy problem for linear elasticity in two dimentional ...a problem may be formulated as follows: given the displacement and one component of the traction in a given part of the boundary ...
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Existence and uniqueness to the Cauchy problem for linear and semilinear parabolic equations with local conditions⋆
... the Cauchy problem in R d for a class of semilinear parabolic partial differ- ential equations that arises in some stochastic control ...with linear parabolic equations. The linear equations ...
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Rank two solutions of the abstract Cauchy problem
... In Problem (E), A and B are densely defined linear operators on X ...then Problem (E ) is called degenerate problem, otherwise it is called ...then Problem (E) is homogenous, otherwise ...
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Conformable fractional semigroups of operators
... a linear operator of an appropriate type, x ∈ X is given and u : [0, ∞) −→ X is the unknown ...the abstract Cauchy ...the abstract Cauchy problem, we refer to [9], see also ...
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A second order impulsive Cauchy problem
... an abstract second-order impul- sive Cauchy problem modeled in the form ¨ u(t) = Au(t)+ f (t, u(t), u(t)), t ˙ ∈ (−T 0 , T 1 ), t ≠ t i ; u(0) = x 0 , u(0) ˙ = y 0 ; u(t i ) = I i 1 (u(t i )), u(t ˙ ...
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Cauchy Problem of the Singularly Perturbed Sixth Order Boussinesq Type Equation
... [4] Feng, Z.S. (2003) Traveling Solitary Wave Solutions to the Generalized Boussinesq Equation. Wave Motion , 37, 17-23. https://doi.org/10.1016/S0165-2125(02)00019-7 [5] Song, C., Li, H. and Li, J. (2013) Initial ...
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Finite Element Solution of a Problem for Gravity Gyroscopic Equation in the Time Domain
... this conservation law can be obtained from identity (4) by simple manipulations assuming ϑ = u . The same conservation law holds for the Cauchy problem solution of Equation (1) in the entire plane ( x x 1 , ...
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Navier Stokes Equations—Millennium Prize Problems
... In this work, we present final solving Millennium Prize Problems formulated by Clay Math. Inst., Cambridge. A new uniform time estimation of the Cauchy problem solution for the Navier-Stokes equations is ...
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Uniform Asymptotic Solutions of the Cauchy Problem for a Generalized Model Equation of L.S.Pontryagin in the Case of Violation of Conditions of Asymptotic Stability
... This problem was first considered by a graduate student [1] of academician L.S.Pontryagin and bounded ness are proved of solution on the interval t∈[–1, 1]. Here it is constructed a uniform asymptotic expansion of ...
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Global 1 Estimation of the Cauchy Problem Solutions to the Navier Stokes Equation
... Numerous studies of the Navier-Stokes equations have been devoted to the problem of the smoothness of its solu- tions. A good overview of these studies is given in [13]-[17]. The spatial differentiability of the ...
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Existence of solutions of abstract non-autonomous second order integro-differential equations
... In this section we study the existence of solutions for problem (.)-(.). Throughout this section we assume that the hypotheses of Theorem ., Theorem . or Theorem . are satisfied including condition (H). ...
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A Cauchy Kowalevsky theorem for overdetermined systems of nonlinear partial differential equations and geometric applications
... The main motivation for the work presented in this paper is to construct real hypersur- faces in C n+1 with maximal Levi number (see below for the definition), a problem that has been open since Levi numbers were ...
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Existence of solutions for neutral functional mixed volterra integrodifferential evolution equations with nonlocal conditions
... Abstract neutral differential equations arise in many areas of applied mathematics. As such, they have been largely studied during the last few decades. The literature related to ordinary neutral differential ...
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Finite Speed of the Perturbation Distribution and Asymptotic Behavior of the Solutions of a Parabolic System not in Divergence Form
... In this paper we study asymptotic behavior of self-similar solutions for a degenerate parabolic system not in divergence form (1) for slow and the fast diffusion cases. And based on comparison method the property FSPD of ...
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