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1.
Summary This paper extends some earlier results on difference sets andB
2 sequences bySinger, Bose, Erd?s andTuran, andChowla.
This research was supported in part by the United States Air Force through the Air Force Office of Scientific Research of
the Air Research and Development Command, under Contract No. AF 49 (638)-213. Reproduction in whole or part is permitted for
any purpose of the United States Government. 相似文献
2.
F. J. Bureau 《Annali di Matematica Pura ed Applicata》1960,51(1):225-299
Summary Finite part and logarithmic part of some divergent integrals with applications to theCauchy problem.
A Giovanni Sansone nel suo 70mo compleanno.
The research reported in this document has been sponsored in part by the Air Force Office of Scientific Research of the Air
Research and Development Command, United States Air Force, through its European Office under Contract AF 61 (056)-86. 相似文献
3.
Robert W. Carroll 《Annali di Matematica Pura ed Applicata》1961,56(1):1-31
Summary Existence and uniqueness theorems for some generalizedEuler-Poisson-Darboux equations are proved and growth and convexity properties of the solutions are studied for multiply subharmonic initial values.
This research was supported in part by the United States Air Force through the Air Force Office of Scientific Research of
the Air Research and Development Command under Contract No. AF 49 (638)-228, at the University of Maryland, and in part by
the National Science Foundation, under a fellowship grant. 相似文献
4.
Summary In this paper the case of generalized Goursat data is considered for the non-linear partial differential equation Δu = f(x,
y, u, ux, uy). The existence and uniqueness of a solution is demonstrated, under certain conditions, by employing the contraction mapping
method in a suitable Banach space.
This research was supported in part at the Institute for Fluid Dynamics and Applied Mathematics, University of Maryland, by
the National Science Foundation under Grants GP-2067, GP-3937, and in part by the Air Force Office of Scientific Research
under Grant AFOSR 400-64, and at Georgetown University, Washington, D.C., by the National Science Foundation under Grant GP-1650
and GP-5023. 相似文献
5.
F. J. Bureau 《Annali di Matematica Pura ed Applicata》1961,55(1):323-388
Summary The method of singularities is used to solve theCauchy problem for simple hyperbolic partial differential equations, namely, the wave equation and the damped wave equation. The
representation formula for the solution of theCauchy problem is written in terms of finite parts and logarithmic parts of certain divergent integrals.
A process of analytic continuation is also used to solve theCauchy problems under consideration. However, to obtain explicitly the representation formulas for the solutions, one must actually
perform the analytic continuation. It is shown that this is best achieved by making use of finite and logarithmic parts.
Simple examples were purposely chosen so as to show that consideration of finite and logarithmic parts is naturally unavoidable
and ? in the very nature of things ?.
To Enrico Bompiani on his scientific Jubilee.
This work was sponsored in part by the Air Force Office of Scientific Research of the Air Research and Development Command,
United States Air Force, through its European Office. 相似文献
6.
Summary A bilinear divergence identity is obtained, which differs from the usualLagrange divergence identity employed byRiemann. In the case of two independent variables, this new identity is used to unify the treatment ofCauchy's problem for hyperbolic equations, the initial value problem for parabolic equations, and theDirichlet problem for elliptic equations.
This research was supported in whole or in part by the United States Air Force under Contract No. AF18(600)-573 monitored by the Office of Scientific Research, Air Research and Development Command. 相似文献
7.
Summary The explicit solution of a particularCauchy problem for the n-dimensionalEuler-Poisson-Darboux equation is found. To obtain the solution the method ofM. Riesz is extended to include non self-adjoint equations. Existence and uniqueness are shown.
This research was supported in part by the United States Air Force under Contract No. AF18(600)-573 — monitored by the Office
of Scientific Research, Air Research and Development Command. 相似文献
8.
Alexander Weinstein 《Annali di Matematica Pura ed Applicata》1957,43(1):325-340
Summary Investigation of the Euler-Poisson-Darboux equation for special initial values. Generalized transformation ofTricomi-Cibrario. Extension of classical theorems ofF. Riesz andP. Montel on mean values of subharmonic functions.
This research was supported in part by the United States Air Force under Contract AF 18(600)573 — monitored by the Office
of Scientific Research, Air Research and Development Command. 相似文献
9.
Summary Reflection principles, analogous to the classicalSchwarz reflection principle for harmonic functions, are obtained for solutions of linear elliptic second order partial differential
equations with constant coefficients. The boundary conditions employed are supposed to be satisfied in a limiting sense only,
and do not require (a priori) the existence of derivatives on the boundary.
To Mauro Picone on his 70th birth day.
This research was supported in part by the United States Air Force under Contract No. AF(600)-573 — monitored by the Office of Scientific Research, Air Research and Development Command.
The work of this author was sponsored by the Office of Ordnance Research, U.S. Army, under the Contract DA-36-034-ORD-1486. 相似文献
10.
J. B. Diaz 《Annali di Matematica Pura ed Applicata》1960,52(1):163-181
Summary After a preliminary survey of related results, a general uniqueness theorem for the ordinary differential equation dy/dx=f(x,
y) is given in section 4. The general uniqueness theorem for the hyperbolic partial differential equation uxy=f(x, y, u), proved in section 5, is an exact analogue of the general uniqueness theorem for the ordinary differential equation
dy/dx=f(x, y).
This research was supported in part by the United States Air Force through the Air Force Office of Scientific Research and
Development Command under Contract No. AF 49(638)-228.
This is a detailed account of lectures given at the Sixth Conference of Arsenal Mathematicians, held at Duke University Durham,
North Carolina, June 1, 2, 1960, and at the Symposium on the Numerical Treatment of Ordinary Differential Equations, Integral
and Integro-Differential Equations, Rome, 20–24 September 1960. 相似文献
11.
Alexander Weinstein 《Annali di Matematica Pura ed Applicata》1962,60(1):87-91
Summary Extension of theorems ofF. Riesz on subharmonic functions to spaces of constant curvature by the use of hyperbolic partial differential equations.
To Enrico Bompiani on his scientific Jubiles
This research was supported in part by the United States Air Force through the Air Force Office of Scientific Research of
the Air Research and Development Command under ontract No. AF 49 (638)–228. 相似文献
12.
Hongfei Zhang 《Applicable analysis》2013,92(1-4):107-137
The singular diffusion equation ut=(u?1ux)x:arises in many areas of application, e.g. in the central limit approximation to Carleman's model of Boltzman equation, or, in the expansion of a thermalized electron cloud in plasma physics. This paper concerns the existence and uniqueness of solution of a mixed boundary value problem of equation ut=(um=1ux)x for ?1 < m ≤0. 相似文献
13.
Carlo Pucci 《Annali di Matematica Pura ed Applicata》1959,48(1):161-172
Sunto Si discute il problema diCauchy relativo all'equazione del calore, ut=uxx, ed a condizioni iniziali sull'asse t. Si provano inoltre alcune proprietà delle soluzioni positive di tale problema e di
analoghi problemi diCauchy relativi a più generali equazioni paraboliche.
A Giovanni Sansone nel suo 70mo compleanno. 相似文献
Summary We consider theCauchy problem for the heat equation, ut=uxx, with initial conditions on the t-axis. We prove some property of positive solutions of this problem, and of similarCauchy problems for more general parabolic equations.
A Giovanni Sansone nel suo 70mo compleanno. 相似文献
14.
Ohne ZusammenfassungThis research was supported in part (as far as the work ofW. Jurkat is concerned) by the United States Air Force, through the Office of Scientific Research of the Air Research and Development Command. 相似文献
15.
Representations for the solution of the Zakai equation in terms of multiple Stratonovich integrals are derived. A new semigroup
(the Feynman-Stratonovich semigroup) associated with the Zakai equation is introduced and using the relationship between multiple
Stratonovich integrals and iterated Stratonovich integrals, a representation for the unnormalized conditional density,u(t,x), solely in terms of the initial density and the semigroup, is obtained. In addition, a Fourier seriestype representation
foru(t,x) is given, where the coefficients in this representation uniquely solve an infinite system of partial differential equations.
This representation is then used to obtain approximations foru(t,x). An explicit error bound for this approximation, which is of the same order as for the case of multiple Wiener integral
representations, is obtained.
Research supported by the National Science Foundation and the Air Force Office of Scientific Research Grant No. F49620 92
J 0154 and the Army Research Office Grant No. DAAL03-92-G0008. 相似文献
16.
Separation of variables of a generalized porous medium equation with nonlinear source 总被引:2,自引:0,他引:2
P.G. Estévez Changzheng QuShunli Zhang 《Journal of Mathematical Analysis and Applications》2002,275(1):44-59
This paper considers a general form of the porous medium equation with nonlinear source term: ut=(D(u)uxn)x+F(u), n≠1. The functional separation of variables of this equation is studied by using the generalized conditional symmetry approach. We obtain a complete list of canonical forms for such equations which admit the functional separable solutions. As a consequence, some exact solutions to the resulting equations are constructed, and their behavior are also investigated. 相似文献
17.
R. Bruce Kellogg 《Journal of Differential Equations》2010,248(1):184-208
The semilinear reaction-diffusion equation −ε2Δu+b(x,u)=0 with Dirichlet boundary conditions is considered in a convex polygonal domain. The singular perturbation parameter ε is arbitrarily small, and the “reduced equation” b(x,u0(x))=0 may have multiple solutions. An asymptotic expansion for u is constructed that involves boundary and corner layer functions. By perturbing this asymptotic expansion, we obtain certain sub- and super-solutions and thus show the existence of a solution u that is close to the constructed asymptotic expansion. The polygonal boundary forces the study of the nonlinear autonomous elliptic equation −Δz+f(z)=0 posed in an infinite sector, and then well-posedness of the corresponding linearized problem. 相似文献
18.
Alexander Weinstein 《Annali di Matematica Pura ed Applicata》1955,39(1):245-254
Summary The general solution for a class of equations of even order is expressed as a sum of solutions of equations of second order.
To Mauro Picone on his 70th birthday.
This research was supported in part by the United States Air Force under Contract No. AF(600)-573 — monitored by the Office of Scientific Research, Air Research and Development Command. 相似文献
19.
Alberto Bressan 《Bulletin of the Brazilian Mathematical Society》2016,47(1):157-169
For some classes of one-dimensional nonlinear wave equations, solutions are Hölder continuous and the ODEs for characteristics admit multiple solutions. Introducing an additional conservation equation and a suitable set of transformed variables, one obtains a new ODE whose right hand side is either Lipschitz continuous or has directionally bounded variation. In this way, a unique characteristic can be singled out through each initial point. This approach yields the uniqueness of conservative solutions to various equations, including the Camassa-Holm and the variational wave equation utt ? c(u)(c(u)ux )x = 0, for general initial data in H1(R). 相似文献
20.
Summary In this paper, we show that there exists a sequence of rational functions of the formR
n(z)=pn–1(z)/(1+z/n)n,n=1, 2, ..., with degp
n–1n–1, which converges geometrically toe
–z in the uniform norm on [0, +), as well as on some infinite sector symmetric about the positive real axis. We also discuss the usefulness of such rational functions in approximating the solutions of heat-conduction type problems.Research supported in part by the Air Force Office of Scientific Research under Grant AFOSR-74-2688, and by the University of South Florida Research Council.Research supported in part by the Air Force Office of Scientific Research under Grant AFOSR-74-2729, and by the Energy Research and Development Administration (ERDA) under Grant E(11-1)-2075. 相似文献