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1.
Peter Ebenfelt 《偏微分方程通讯》2013,38(11-12):2129-2151
In this paper, we study holomorphic solutions of overdetermined systems of partial differential equatoins with constant coefficients. We parametrize the solution space, using an ideal of holomorphic functions generated by certain polynomials associated to the principal symbols of the operators, by proving a Cauchy-Kowalevsky type theorem for these systems. In this theorem, we introduce a non-characteristicity condition for systems which is a direct generalization of a condition for single equations introduced by the author and H.S. Shapiro in a previous paper. As a tool for studying the systems mentioned above, certain estimates, which may be of independent interest, for elements of analytic modules generated by polynomials are obtained. 相似文献
2.
Shuhong Gao. 《Mathematics of Computation》2003,72(242):801-822
A new method is presented for factorization of bivariate polynomials over any field of characteristic zero or of relatively large characteristic. It is based on a simple partial differential equation that gives a system of linear equations. As in Berlekamp's and Niederreiter's algorithms for factoring univariate polynomials, the dimension of the solution space of the linear system is equal to the number of absolutely irreducible factors of the polynomial to be factored, and any basis for the solution space gives a complete factorization by computing gcd's and by factoring univariate polynomials over the ground field. The new method finds absolute and rational factorizations simultaneously and is easy to implement for finite fields, local fields, number fields, and the complex number field. The theory of the new method allows an effective Hilbert irreducibility theorem, thus an efficient reduction of polynomials from multivariate to bivariate.
3.
By means of a method of analytic number theory the following theorem is proved. Letp be a quasi-homogeneous linear partial differential operator with degreem,m > 0, w.r.t a dilation
given by ( a1, …, an). Assume that either a1, …, an are positive rational numbers or
for some
Then the dimension of the space of polynomial solutions of the equationp[u] = 0 on ℝn must be infinite 相似文献
4.
Solutions to nonlinear partial differential equations of fourth order are studied. Boundary regularity is proved for solutions
that satisfy mixed boundary conditions. Various geometric situations including so called triple points are considered. Regularity is measured in Sobolev-Slobodeckii spaces and the results are sharp in this scale. The approach
is based on the use of a first order difference quotient method. 相似文献
5.
Xicheng Zhang 《Journal of Functional Analysis》2007,249(2):454-476
In this paper, we study the regularities of solutions to semilinear stochastic partial differential equations in general settings, and prove that the solution can be smooth arbitrarily when the data is sufficiently regular. As applications, we also study several classes of semilinear stochastic partial differential equations on abstract Wiener space, complete Riemannian manifold as well as bounded domain in Euclidean space. 相似文献
6.
David Nualart Lluís Quer-Sardanyons 《Stochastic Processes and their Applications》2009,119(11):3914-3938
In this paper we establish lower and upper Gaussian bounds for the solutions to the heat and wave equations driven by an additive Gaussian noise, using the techniques of Malliavin calculus and recent density estimates obtained by Nourdin and Viens in [17]. In particular, we deal with the one-dimensional stochastic heat equation in [0, 1] driven by the space-time white noise, and the stochastic heat and wave equations in Rd (d≥1 and d≤3, respectively) driven by a Gaussian noise which is white in time and has a general spatially homogeneous correlation. 相似文献
7.
8.
A Liouville-Green (or WKB) asymptotic approximation theory is developed for the class of linear second-order matrix differential equations Y″=[f(t)A+G(t)]Y on [a,+∞), where A and G(t) are matrices and f(t) is scalar. This includes the case of an “asymptotically constant” (not necessarily diagonalizable) coefficient A (when f(t)≡1). An explicit representation for a basis of the right-module of solutions is given, and precise computable bounds for the error terms are provided. The double asymptotic nature with respect to both t and some parameter entering the matrix coefficient is also shown. Several examples, some concerning semi-discretized wave and convection-diffusion equations, are given. 相似文献
9.
Masafumi Yoshino 《Mathematische Nachrichten》2006,279(11):1242-1263
We solve a Fuchsian system of singular nonlinear partial differential equations with resonances. These equations have no smooth solutions in general. We show the solvability in a class of finitely smooth functions. Typical examples are a homology equation for a vector field and a degenerate Monge–Ampère equation. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
10.
Bahriye Karaca 《复变函数与椭圆型方程》2020,65(10):1748-1762
ABSTRACT Complex model partial differential equations of arbitrary order are considered. The uniqueness of the Dirichlet problem is studied. It is proved that the Dirichlet problem for higher order complex partial differential equations with one complex variable has infinitely many solutions. 相似文献
11.
Eduardo Hernández M. Marco Rabello 《Journal of Mathematical Analysis and Applications》2007,331(2):1135-1158
This paper is concerned with partial neutral functional differential equations of first and second order with impulses. We establish some results of existence of mild solutions for these classes of equations. 相似文献
12.
A. K. Kapikyan V. B. Levenshtam 《Computational Mathematics and Mathematical Physics》2008,48(11):2059-2076
Systems of first-order semilinear partial differential equations with terms that oscillate at a frequency ω ? 1 in a single variable and are proportional to \(\sqrt \omega \) are considered. The Krylov-Bogolyubov-Mitropol’skii averaging method is substantiated for such equations. Based on the two-scale expansion method, an algorithm for constructing complete asymptotics of solutions is proposed and justified. 相似文献
13.
Xiao-Bao Shu Yongzeng LaiYuming Chen 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(5):2003-2011
This paper is concerned with the existence of mild solutions for a class of impulsive fractional partial semilinear differential equations. Some errors in Mophou (2010) [2] are corrected, and some previous results are generalized. 相似文献
14.
Tropical differential equations are introduced and an algorithm is designed which tests solvability of a system of tropical linear differential equations within the complexity polynomial in the size of the system and in the absolute values of its coefficients. Moreover, we show that there exists a minimal solution, and the algorithm constructs it (in case of solvability). This extends a similar complexity bound established for tropical linear systems. In case of tropical linear differential systems in one variable a polynomial complexity algorithm for testing its solvability is designed.We prove also that the problem of solvability of a system of tropical non-linear differential equations in one variable is NP-hard, and this problem for arbitrary number of variables belongs to NP. Similar to tropical algebraic equations, a tropical differential equation expresses the (necessary) condition on the dominant term in the issue of solvability of a differential equation in power series. 相似文献
15.
The stability of abstract stochastic partial differential equations with respect to the simultaneous perturbation of the driving processes and of the differential operators is investigated. The results obtained here will be applied to concrete stochastic partial differential equations in the continuation of this paper 相似文献
16.
A. A. Shlapunov 《Siberian Advances in Mathematics》2007,17(2):144-152
We obtain some conditions of solvability in Sobolev spaces for the systems of linear partial differential equations and deduce the corresponding formulas for solutions to these systems. The solutions are given as the sum of the series whose terms are the iterations of some pseudodifferential operators constructed explicitly. 相似文献
17.
18.
This paper first provides a common framework for partial differential equation problems in both strong and weak form by rewriting
them as generalized interpolation problems. Then it is proven that any well-posed linear problem in strong or weak form can
be solved by certain meshless kernel methods to any prescribed accuracy.
The work described in this paper was partially supported by a grant from the Research Grants Council of the Hong Kong Special
Administrative Region, China (Project No. CityU 101205). Robert Schaback’s research in Hong Kong was sponsored by DFG and
City University of Hong Kong. 相似文献
19.
Summary Stochastic evolution equations with monotone operators in Banach spaces are considered. The solutions are characterized as
minimizers of certain convex functionals. The method of monotonicity is interpreted as a method of constructing minimizers
to these functionals, and in this way solutions are constructed via Euler-Galerkin approximations. 相似文献
20.
一类二阶中立型偏泛函微分方程组解的振动性 总被引:7,自引:2,他引:7
林文贤 《纯粹数学与应用数学》2003,19(3):263-267
获得了一类二阶中立型偏泛函微分方程组解振动的若干充分条件. 相似文献