共查询到20条相似文献,搜索用时 10 毫秒
1.
Hui-Sheng Ding Wei Long Gaston M. NGurkata 《Nonlinear Analysis: Theory, Methods & Applications》2009,70(12):4158-4164
In this paper, we establish some new theorems about the existence of almost automorphic solutions to nonautonomous evolution equations u′(t)=A(t)u(t)+f(t) and u′(t)=A(t)u(t)+f(t,u(t)) in Banach spaces. As we will see, our results allow for a more general A(t) to some extent. An example is also given to illustrate our results. In addition, by means of an example, we show that one cannot ensure the existence of almost automorphic solutions to u′(t)=A(t)u(t)+f(t) even if the evolution family U(t,s) generated by A(t) is exponentially stable and fAA(X). 相似文献
2.
We consider the problem of simultaneously determining coefficients of a second order nonlinear parabolic equation and a solution to this equation. The unknown coefficients occur in the main part and in the nonlinear summand as well. The overdetermination conditions are conditions of the Dirichlet type on a family of planes of arbitrary dimension. It is demonstrated that the problem in question is solvable locally in time in Hölder spaces. When the unknown functions enter the right-hand side and the equation is linear, the theorem of global unique existence (in time) is established. 相似文献
3.
Bogdan Sasu 《Journal of Mathematical Analysis and Applications》2006,323(2):1465-1478
The aim of this paper is to give characterizations for uniform and exponential dichotomies of evolution families on the half-line. We associate with a discrete evolution family Φ={Φ(m,n)}(m,n)∈Δ the subspace . Supposing that X1 is closed and complemented, we prove that the admissibility of the pair implies the uniform dichotomy of Φ. Under the same hypothesis on X1, we obtain that the admissibility of the pair with p∈(1,∞] is a sufficient condition for the exponential dichotomy of Φ, which becomes necessary when Φ is with exponential growth. We apply our results in order to deduce new characterizations for exponential dichotomy of evolution families in terms of the solvability of associated difference and integral equations. 相似文献
4.
Hui-Sheng Ding Jin Liang Gaston M. N’Guérékata Ti-Jun Xiao 《Nonlinear Analysis: Theory, Methods & Applications》2007
This paper is concerned with pseudo-almost periodicity of the solutions to the nonautonomous evolution equation with delay u′(t)=A(t)u(t)+f(t,u(t−h)). Some sufficient conditions which ensure the existence and uniqueness of pseudo-almost periodic mild solutions to the evolution equation with delay are given. An example is shown to illustrate our results. 相似文献
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6.
Marta Tyran-Kamińska 《Mathematical Methods in the Applied Sciences》2020,43(18):10511-10531
We provide a new perturbation theorem for substochastic semigroups on abstract AL spaces extending Kato's perturbation theorem to nondensely defined operators. We show how it can be applied to piecewise deterministic Markov processes and transport equations with abstract boundary conditions. We give particular examples to illustrate our results. 相似文献
7.
We study the relationship between the Dirichlet problem and the Cauchy problem with inhomogeneous boundary conditions for
local operators. Our results are applied to non-autonomous parabolic problems on non-cylindrical domains.
Received January 10, 2001; accepted April 5, 2001. 相似文献
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9.
This paper establishes a global Carleman inequality of parabolic equations with mixed boundary conditions and an estimate of the solution. Further, we prove exact controllability of the equation by controls acting on an arbitrarily given subdomain or subboundary. 相似文献
10.
The initial-boundary value problems for parabolic equations with variable exponents of nonlinearity and time depended delay are considered. Existence and uniqueness of solutions of these problems are proved. 相似文献
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12.
The stability of difference schemes for one-dimensional and two-dimensional parabolic equations, subject to non-local (Bitsadze-Samarskii type) boundary conditions is dealt with. To analyze the stability of difference schemes, the structure of the spectrum of the matrix that defines the linear system of difference equations for a respective stationary problem is studied. Depending on the values of parameters in non-local conditions, this matrix can have one zero, one negative or complex eigenvalues. The stepwise stability is proved and the domain of stability of difference schemes is found. 相似文献
13.
Xianzhong Zeng 《Journal of Mathematical Analysis and Applications》2007,332(2):1408-1424
This paper deals with the critical exponents for the quasi-linear parabolic equations in Rn and with an inhomogeneous source, or in exterior domains and with inhomogeneous boundary conditions. For n?3, σ>−2/n and p>max{1,1+σ}, we obtain that pc=n(1+σ)/(n−2) is the critical exponent of these equations. Furthermore, we prove that if max{1,1+σ}<p?pc, then every positive solution of these equations blows up in finite time; whereas these equations admit the global positive solutions for some f(x) and some initial data u0(x) if p>pc. Meantime, we also demonstrate that every positive solution of these equations blows up in finite time provided n=1,2, σ>−1 and p>max{1,1+σ}. 相似文献
14.
R. Quintanilla 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2006,57(4):595-603
In this note we investigate the spatial behavior of several nonlinear parabolic equations with nonlinear boundary conditions.
Under suitable conditions on the nonlinear terms we prove that the solutions either cease to exist for a finite value of the
spatial variable or else they decay algebraically. The main tool used is the weighted energy method. Our results can be applied
to several situations concerning heat conduction.
Received: April 4, 2004; revised: September 20, 2004 相似文献
15.
We consider an initial-boundary value problem for a one-dimensional parabolic equation with nonlocal boundary conditions. These nonlocal conditions are given in terms of integrals. Based on solution of the Dirichlet problem for the parabolic equation, we constructively establish the well-posedness for the nonlocal problem. 相似文献
16.
Xuan-ru Lu Guang-Hua Gao Zhi-Zhong Sun 《Numerical Methods for Partial Differential Equations》2023,39(1):447-480
In this paper, the fourth-order parabolic equations with different boundary value conditions are studied. Six kinds of boundary value conditions are proposed. Several numerical differential formulae for the fourth-order derivative are established by the quartic interpolation polynomials and their truncation errors are given with the aid of the Taylor expansion with the integral remainders. Effective difference schemes are presented for the third Dirichlet boundary value problem, the first Neumann boundary value problem and the third Neumann boundary value problem, respectively. Some new embedding inequalities on the discrete function spaces are presented and proved. With the method of energy analysis, the unique solvability, unconditional stability and unconditional convergence of the difference schemes are proved. The convergence orders of derived difference schemes are all O(τ2 + h2) in appropriate norms. Finally, some numerical examples are provided to confirm the theoretical results. 相似文献
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18.
È. M. Saydamatov 《Siberian Advances in Mathematics》2007,17(3):213-226
In the article we study the questions of well-posedness of general nonlocal boundary value problems for pseudodifferential equations in the Besov-type limit spaces. 相似文献
19.
For the numerical solution of high even order differential equations with two-points Hermite boundary conditions a general collocation method is derived and studied. Computation of the integrals which appear in the coefficients are generated by a recurrence formula and no integrals are involved in the calculation. An application to the solution of the beam problem is given. Numerical experiments provide favorable comparisons with other existing methods. 相似文献
20.
We consider the evolution equation whose right-hand side is the sum of a linear unbounded operator generating a compact strongly
continuous semigroup and a continuous operator acting in function spaces. We prove the existence of a solution that stays
within a given closed convex set and moreover, satisfies a functional boundary condition, particular cases of which are the
Cauchy initial condition, periodicity condition, mixed condition including continuous transformations of spatial variables,
etc. The main result is illustrated by using an example of the boundary-value problem for a partial operator-differential
equation.
Translated fromMatematicheskie Zametki, Vol. 65, No. 1, pp. 48–60, January, 1999. 相似文献