Leray arbejde på Cauchy problem førte ham til at studere rester teori. I to papirer Kumano-Go desuden studeret ikke-unikke løsninger af Cauchy problem.
In two papers Kumano-Go also studied non-uniqueness of solutions of the Cauchy problem.Vi foreslår at studere globalt den lineære Cauchy problem i den komplekse sag, så i den virkelige hyperbolsk tilfældet, hvis det antages, at de givne oplysninger er analytisk.
We propose to study globally the linear Cauchy problem in the complex case, then in the real hyperbolic case, assuming that the given data is analytic.Han studerede tid afhængige hyperbolsk partielle differentialligninger ogogså begyndte at arbejde på Cauchy problem.
He studied time dependent hyperbolic partial differential equations andalso began to work on the Cauchy problem.Han har også opnået nogle grundlæggende resultater i solvens af Cauchy problem for erhvervsdrivende ligninger i Banachrum.
He also obtained some basic results in the solvability of the Cauchy problem for operator equations in Banach spaces.I 1959 han:… udviklet en generel restkoncentrationer teori om komplekse manifolds og anvender den til undersøgelse afkonkrete integrals afhængigt af parametre, der skyldes løse Cauchy problem.
In 1959 he:… developed a general residue theory on complex manifolds andapplied it to the investigation of concrete integrals depending on parameters arising from solving the Cauchy problem.I 1958 Calderón offentliggjort en af hans vigtigste resultater på enestående i Cauchy problem for partielle differentialligninger.
In 1958 Calderón published one of his most important results on uniqueness in the Cauchy problem for partial differential equations.Den revolutionære karakter af disse værker er afspejlet i det faktum, at J Hadamard, en verden myndighed på det pågældende tidspunkt,afsættes et særligt tillæg til Lewy's teori i sin nyligt udgivet bog om Cauchy Problem 1932.
The revolutionary character of these works is reflected in the fact that J Hadamard, a world authority at that time,devoted a special appendix to Lewy's theory in his newly published book on the Cauchy Problem 1932.For hyperbolsk ligninger,konstruere konvergerende forskel ordninger for Cauchy problem, og for første grænseoverskridende problemer..
For hyperbolic equations,construct convergent difference schemes for the Cauchy problem and for initial-boundary problems..I 1991 blev han tildelt National Medal of Science og igen,han arbejder på enestående i Cauchy problem blev citeret.
In 1991 he was awarded the National Medal of Science andagain he work on uniqueness in the Cauchy problem was cited.Således er hans forskning i jordskorpen føre til undersøgelser på godt stillet Cauchy problemer for Parabolic ligninger og til opførelse af en metode til at løse almindelige funktionelle ligninger af Volterra type.
Thus, his research on the Earth's crust lead to investigations on well-posed Cauchy problems for parabolic equations and to the construction of a method for solving general functional equations of Volterra type.Han brugte metoder på hinanden tilnærmelse at vise eksistensen af opløsninger af ordinære differentialligninger løse Cauchy problem for disse differentialligninger.
He used methods of successive approximation to show the existence of solutions of ordinary differential equations solving the Cauchy problem for these differential equations.I 1955 De Giorgi gav et vigtigt eksempel, som viste nonuniqueness for løsninger af Cauchy problem for partielle differentialligninger af parabolsk type, hvis coefficents opfylde visse regelmæssighed betingelser.
In 1955 De Giorgi gave an important example which showed nonuniqueness for solutions of the Cauchy problem for partial differential equations of parabolic type whose coefficents satisfy certain regularity conditions.I løbet af disse år Kumano-Go offentliggjort en række papirer, som studerede de lokale ogglobale egenart af de løsninger af Cauchy problem for partielle differentialligninger.
During these years Kumano-Go published a series of papers which studied the local andglobal uniqueness of the solutions of the Cauchy problem for partial differential equations.ARF fremlagt et oplæg om en generalisering af Green's formel og dens anvendelse til Cauchy problem for et hyperbolsk ligning til mængden Studier i matematik og mekanik præsenteret for Richard von Mises i 1954.
Arf presented a paper On a generalization of Green 's formula and its application to the Cauchy problem for a hyperbolic equation to the volume Studies in mathematics and mechanics presented to Richard von Mises in 1954.Han blev tildelt National Medal of Science:… for hans banebrydende arbejde på ental integrerende erhvervsdrivende, der fører til deres anvendelse til vigtige problemer i partielle differentialligninger,herunder hans bevis for enestående i Cauchy problem, Atiyah-Singer indeks sætning, og opformering af singularities i bratte ligninger.
He was awarded the National Medal of Science:… for his ground-breaking work on singular integral operators leading to their application to important problems in partial differential equations,including his proof of uniqueness in the Cauchy problem, the Atiyah-Singer index theorem, and the propagation of singularities in nonlinear equations.ARF fremlagt et oplæg om en generalisering af Green's formel og dens anvendelse til Cauchy problem for et hyperbolsk ligning til mængden Studier i matematik og mekanik præsenteret for Richard von Mises i 1954. ARF havde mødt von Mises i 1933 i Istanbul.
Arf presented a paper On a generalization of Green 's formula and its application to the Cauchy problem for a hyperbolic equation to the volume Studies in mathematics and mechanics presented to Richard von Mises in 1954. Arf had met von Mises in 1933 in Istanbul.For hans banebrydende arbejde på ental integrerende erhvervsdrivende, der fører til deres anvendelse til vigtige problemer i partielle differentialligninger,herunder hans bevis for enestående i Cauchy problem, Atiyah-Singer indeks sætning, og opformering af singularities i bratte ligninger.
For his ground-breaking work on singular integral operators leading to their application to important problems in partial differential equations,including his proof of uniqueness in the Cauchy problem, the Atiyah-Singer index theorem, and the propagation of singularities in nonlinear equations.I 1957 blev han forklarede formålet med hans arbejde på dette område:Vi foreslår at studere globalt den lineære Cauchy problem i den komplekse sag, så i den virkelige hyperbolsk tilfældet, hvis det antages, at de givne oplysninger er analytisk.
In 1957 he explained the aims of his work in this area:We propose to study globally the linear Cauchy problem in the complex case, then in the real hyperbolic case, assuming that the given data is analytic.I samme periode fik hun formler, der gjorde det muligt at beregne i simple algebraiske termer den numeriske parametre, der afgør klasser af unikke og godt-posedness af Cauchy problem for systemer af lineære partielle differentialligninger med konstante koefficienter.
In the same period she obtained formulae that made it possible to compute in simple algebraic terms the numerical parameters that determine classes of uniqueness and well-posedness of the Cauchy problem for systems of linear partial differential equations with constant coefficients.
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Time: 0.0301
Den tilsvarende skalar Cauchy problem, der involverer denne funktion i stedet for Ai-og b har et eksplicit lokale analytisk løsning.
Så er der et kvarter af 0 i W, som quasilinear Cauchy problem
med startbetingelse
på hyperoverflade
har en unik analytisk løsning ƒ: W → V nær 0.
Time machines and the Principle of Self-Consistency as a Consequence of the Principle of Stationary Action (II): The Cauchy Problem for a Self-Interacting Relativistic Particle
Carlini, A. & Novikov, I.
Højere ordens Cauchy-Kowalevski teorem
Hvis F og fj er analytiske funktioner nærheden 0, så den ikke-lineære Cauchy problem
med begyndelsesbetingelser
har en unik analytisk løsning nær 0.
At my online A Cauchy problem I will now result 1:15.
Solution of Cauchy problem using method of characteristics.
The Cauchy problem in general relativity (pdf).
Cauchy problem for equations with loadings on surfaces // Ukr.
Cauchy problem for a semilinear Éidel’man parabolic equation // Ukr.
We consider the Cauchy problem for the critical Burgers equation.
The Cauchy problem for the differential operator a x,.
Suslov. "The Cauchy problem for a forced harmonic oscillator." Rev.
Cauchy Problem in Spacetimes with Closed Timelike Curves.
The Cauchy problem for the B-wave system // Ukr.
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