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排序方式: 共有275条查询结果,搜索用时 15 毫秒
1.
We study initial boundary value problems for linear scalar evolutionpartial differential equations, with spatial derivatives ofarbitrary order, posed on the domain {t > 0, 0 < x <L}. We show that the solution can be expressed as an integralin the complex k-plane. This integral is defined in terms ofan x-transform of the initial condition and a t-transform ofthe boundary conditions. The derivation of this integral representationrelies on the analysis of the global relation, which is an algebraicrelation defined in the complex k-plane coupling all boundaryvalues of the solution. For particular cases, such as the case of periodic boundaryconditions, or the case of boundary value problems for even-orderPDEs, it is possible to obtain directly from the global relationan alternative representation for the solution, in the formof an infinite series. We stress, however, that there existinitial boundary value problems for which the only representationis an integral which cannot be written as an infinite series.An example of such a problem is provided by the linearized versionof the KdV equation. Similarly, in general the solution of odd-orderlinear initial boundary value problems on a finite intervalcannot be expressed in terms of an infinite series. 相似文献
2.
Vincenzo Recupero 《Journal of Mathematical Analysis and Applications》2004,300(2):387-407
In this paper we study a model of phase relaxation for the Stefan problem with the Cattaneo–Maxwell heat flux law. We prove an existence and uniqueness result for the resulting problem and we show that its solution converges to the solution of the Stefan problem as the two relaxation parameters go to zero, provided a relation between these parameters holds. 相似文献
3.
Cheikh Birahim Ndiaye 《Journal of Functional Analysis》2007,251(1):1-58
Working in a given conformal class, we prove existence of constant Q-curvature metrics on compact manifolds of arbitrary dimension under generic assumptions. The problem is equivalent to solving a nth-order non-linear elliptic differential (or integral) equation with variational structure, where n is the dimension of the manifold. Since the corresponding Euler functional is in general unbounded from above and below, we use critical point theory, jointly with a compactness result for the above equation. 相似文献
4.
We present a unified approach for linear and nonlinear sensitivity analysis for models of reaction kinetics that are stated in terms of systems of ordinary differential equations (ODEs). The approach is based on the reformulation of the ODE problem as a density transport problem described by a Fokker-Planck equation. The resulting multidimensional partial differential equation is herein solved by extending the TRAIL algorithm originally introduced by Horenko and Weiser in the context of molecular dynamics (J. Comp. Chem. 2003, 24, 1921) and discussed it in comparison with Monte Carlo techniques. The extended TRAIL approach is fully adaptive and easily allows to study the influence of nonlinear dynamical effects. We illustrate the scheme in application to an enzyme-substrate model problem for sensitivity analysis w.r.t. to initial concentrations and parameter values. 相似文献
5.
R. Feola F. Iandoli 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2019,36(1):119-164
We prove local in time well-posedness for a large class of quasilinear Hamiltonian, or parity preserving, Schrödinger equations on the circle. After a paralinearization of the equation, we perform several paradifferential changes of coordinates in order to transform the system into a paradifferential one with symbols which, at the positive order, are constant and purely imaginary. This allows to obtain a priori energy estimates on the Sobolev norms of the solutions. 相似文献
6.
A.B. Sow 《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(5):429-477
Using a forward–backward stochastic differential equations (FBSDE) associated to a transmutation process driven by a finite sequence of Poisson processes, we obtain a probabilistic interpretation for a non-degenerate system of quasilinear parabolic partial differential equations (PDEs). The novetly is that the linear second order differential operator is different on each line of the system. 相似文献
7.
Andrea MALCHIODI 《数学年刊B辑(英文版)》2017,38(2):539-562
The author surveys some recent progress on the Toda system on a two-dimensional surface Σ,arising in models from self-dual non-abelian Chern-Simons vortices,as well as in differential geometry.In particular,its variational structure is analysed,and the role of the topological join of the barycentric sets of Σ is shown. 相似文献
8.
The main purpose of this paper is to study the existence of single-peaked positive solutions of the singularly perturbed elliptic equation
9.
Fathi B. Saidp∗ 《Applicable analysis》2013,92(1-4):101-127
We study the existence, uniqueness, and asymtotic behaviour of non-negative solutions to a parabolic diffusion equation involving a nonlocal con-vective term on a bounded domain ? contained in Rn. We apply the In variance Principle of LaSalle and Hale to prove that the solution tends to zero as t → ∞ 相似文献
10.
Daniela Kraus 《Journal of Mathematical Analysis and Applications》2008,345(2):628-631
The precise asymptotic behaviour of the solutions to the two-dimensional curvature equation Δu=k(z)e2u with e2u∈L1 for bounded nonnegative curvature functions −k(z) near isolated singularities is obtained. 相似文献