Displaying similar documents to “On the mixed problem for quasilinear partial functional differential equations with unbounded delay”

On the mixed problem for hyperbolic partial differential-functional equations of the first order

Tomasz Człapiński (1999)

Czechoslovak Mathematical Journal

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We consider the mixed problem for the hyperbolic partial differential-functional equation of the first order D x z ( x , y ) = f ( x , y , z ( x , y ) , D y z ( x , y ) ) , where z ( x , y ) [ - τ , 0 ] × [ 0 , h ] → ℝ is a function defined by z ( x , y ) ( t , s ) = z ( x + t , y + s ) , ( t , s ) ∈ [ - τ , 0 ] × [ 0 , h ] . Using the method of bicharacteristics and the method of successive approximations for a certain integral-functional system we prove, under suitable assumptions, a theorem of the local existence of generalized solutions of this problem.

Almost homoclinic solutions for a certain class of mixed type functional differential equations

Joanna Janczewska (2011)

Annales Polonici Mathematici

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We shall be concerned with the existence of almost homoclinic solutions for a class of second order functional differential equations of mixed type: q ̈ ( t ) + V q ( t , q ( t ) ) + u ( t , q ( t ) , q ( t - T ) , q ( t + T ) ) = f ( t ) , where t ∈ ℝ, q ∈ ℝⁿ and T>0 is a fixed positive number. By an almost homoclinic solution (to 0) we mean one that joins 0 to itself and q ≡ 0 may not be a stationary point. We assume that V and u are T-periodic with respect to the time variable, V is C¹-smooth and u is continuous. Moreover, f is non-zero, bounded, continuous and square-integrable....

Noncharacteristic mixed problems for hyperbolic systems of the first order

Ewa Zadrzyńska

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CONTENTS1. Introduction....................................................................................................................................................52. Notations and preliminaries .........................................................................................................................11 2.1. Function spaces and spaces of distributions............................................................................................11 2.2. Perturbations...

Application of complex analysis to second order equations of mixed type

Guo Chun Wen (1998)

Annales Polonici Mathematici

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This paper deals with an application of complex analysis to second order equations of mixed type. We mainly discuss the discontinuous Poincaré boundary value problem for a second order linear equation of mixed (elliptic-hyperbolic) type, i.e. the generalized Lavrent’ev-Bitsadze equation with weak conditions, using the methods of complex analysis. We first give a representation of solutions for the above boundary value problem, and then give solvability conditions via the Fredholm theorem...

Variations of mixed Hodge structure attached to the deformation theory of a complex variation of Hodge structures

Philippe Eyssidieux, Carlos Simpson (2011)

Journal of the European Mathematical Society

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Let X be a compact Kähler manifold, x ∈ X be a base point and ρ : π 1 ( X , x ) → G L N ( C ) be the monodromy representation of a 𝒞 -VHS. Building on Goldman–Millson’s classical work, we construct a mixed Hodge structure on the complete local ring of the representation variety at ρ and a variation of mixed Hodge structures whose monodromy is the universal deformation of ρ .

On the oscillation of forced second order mixed-nonlinear elliptic equations

Zhiting Xu (2010)

Annales Polonici Mathematici

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Oscillation theorems are established for forced second order mixed-nonlinear elliptic differential equations ⎧ d i v ( A ( x ) | | ∇ y | | p - 1 ∇ y ) + ⟨ b ( x ) , | | ∇ y | | p - 1 ∇ y ⟩ + C ( x , y ) = e ( x ) , ⎨ ⎩ C ( x , y ) = c ( x ) | y | p - 1 y + ∑ i = 1 m c i ( x ) | y | p i - 1 y under quite general conditions. These results are extensions of the recent results of Sun and Wong, [J. Math. Anal. Appl. 334 (2007)] and Zheng, Wang and Han [Appl. Math. Lett. 22 (2009)] for forced second order ordinary differential equations with mixed nonlinearities, and include some known oscillation results in the literature

The diagonal mapping in mixed norm spaces

Guangbin Ren, Jihuai Shi (2004)

Studia Mathematica

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For any holomorphic function F in the unit polydisc Uⁿ of ℂⁿ, we consider its restriction to the diagonal, i.e., the function in the unit disc U of ℂ defined by F(z) = F(z,...,z), and prove that the diagonal mapping maps the mixed norm space H p , q , α ( U ⁿ ) of the polydisc onto the mixed norm space H p , q , | α | + ( p / q + 1 ) ( n - 1 ) ( U ) of the unit disc for any 0 < p < ∞ and 0 < q ≤ ∞.

A new mixed finite element method based on the Crank-Nicolson scheme for Burgers' equation

Xiaohui Hu, Pengzhan Huang, Xinlong Feng (2016)

Applications of Mathematics

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In this paper, a new mixed finite element method is used to approximate the solution as well as the flux of the 2D Burgers’ equation. Based on this new formulation, we give the corresponding stable conforming finite element approximation for the P 0 2 - P 1 pair by using the Crank-Nicolson time-discretization scheme. Optimal error estimates are obtained. Finally, numerical experiments show the efficiency of the new mixed method and justify the theoretical results.

Infinite systems of first order PFDEs with mixed conditions

W. Czernous (2008)

Annales Polonici Mathematici

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We consider mixed problems for infinite systems of first order partial functional differential equations. An infinite number of deviating functions is permitted, and the delay of an argument may also depend on the spatial variable. A theorem on the existence of a solution and its continuous dependence upon initial boundary data is proved. The method of successive approximations is used in the existence proof. Infinite differential systems with deviated arguments and differential integral...