Results 1 to 10 of about 11,284,175 (207)
On the Degenerate Cauchy Problem [PDF]
Canadian Journal of Mathematics, 1965 The problem treated here is an abstract version of the Cauchy problem for an equation of mixed type in the hyperbolic region with initial data on the parabolic line (cf. 2, 3, 5, 11, 13, 14, 15, 16, 21, 27). A more complete bibliography may be found in (3, 5, 18). We begin with the equation (6)(1.1)
Robert W. Carroll, Changlu Wang
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Journal of Differential Equations, 1977 AbstractA new approach is developed for investigating abstract Cauchy problems for first order systems of operator differential equations. Questions of existence, representation, and uniqueness for solutions of these systems are settled. Several applications are given and generalizations and extensions of the method are discussed.
J. A. Donaldson
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The Cauchy problem and Hadamard's example [PDF]
Journal of Mathematical Analysis and Applications, 1977 In 1917, Hadamard [5, p. 331 pointed out that U(X) = sin nx, sinh n.r, is a solution of the Laplace equation for every n and that this proves that the Cauchy problem for the Laplace equation with data on x1 = 0 is not well posed in the Cm-topology. Now we know that a necessary and sufficient condition for the Cauchy problem to be well posed in [w” is ...
Jan Persson
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Approximate solutions to Cauchy problems
Journal of Differential Equations, 1972 where f and u are vector-valued functions of (x, t) in some open subset of a Euclidean space Rn+l. We make no assumptions of analyticity about the data f and u,, . Mainly ‘we assume that f(~, t, u, p) is infinitely differentiable with respect to (x, u, p) and continuous with respect to t and that us is C”.
François Trèves
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A NOTE ON THE ABSTRACT CAUCHY PROBLEM [PDF]
Proceedings of the National Academy of Sciences, 1954 Ralph S. Phillips
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The overdetermined Cauchy problem [PDF]
Annales de l’institut Fourier, 1997 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
BOITI, Chiara, M. NACINOVICH
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Journal of Mathematical Analysis and Applications, 1986 The purpose of this paper is to study the incomplete Cauchy problem \[ (P)\quad u''(t)\in Au(t),\quad ...
Simeon Reich, Esteban I. Poffald
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Cauchy problems and applications [PDF]
Topological Methods in Nonlinear Analysis, 2000 The author studies the Cauchy problem \[ {du\over dt}\in Au,\;t>0,\;u(0)=u_0, \] for \(u:[0,\infty)\to X\), where \(X\) is a real Banach space and \(A\) is a nonlinear multi-valued operator in \(X\) satisfying accretiveness and range conditions. Using the method of lines, the author shows that the problem has a limit solution. Under the hypothesis that
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On the abstract Cauchy problem
Journal of Functional Analysis, 1972 AbstractConditions are found under which the abstract Cauchy problem u′(t) = Au(t), u(0) = u0 has a unique solution for each u0 in a dense subspace of a Banach space X. These conditions are shown to be best possible. In the Hilbert space case, conditions are found under which there is a unique weak solution for each u0in D(A). Corresponding results are
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The Cauchy problem for the Pavlov equation [PDF]
Nonlinearity, 2015 Commutation of multidimensional vector fields leads to integrable nonlinear dispersionless PDEs arising in various problems of mathematical physics and intensively studied in the recent literature. This report is aiming to solve the scattering and inverse scattering problem for integrable dispersionless PDEs, recently introduced just at a formal level,
P. M. Santini +5 more
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