On the stochastic quasi-linear symmetric hyperbolic system
نویسندگان
چکیده
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15 صفحه اولOn quasi-linear stochastic partial differential equations
We prove existence and uniqueness of the solution of a parabolic SPDE in one space dimension driven by space-time white noise, in the case of a measurable drift and a constant diffusion coefficient, as well as a comparison theorem.
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1. Introduction In this work we want to explore the relationship between certain eigenvalue condition for the symbols of first order partial differential operators describing evolution processes and the linear and nonlinear stability of their stationary solutions. Consider the initial value problem for the following general first order quasi-linear system of equations
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where t>0, o o < x < o o , U(t, x)=(u(t, x), v(t, x)), and the function F(U)= (f(u, v), g(u, v)) is smooth. GLIMM [2] has proved existence of a weak solution provided that the variation of the initial data Uo(x) is small. GLIMM & LAX [3] then improved this result by requiring that the oscillation of Uo(x) be small. SMOLLER [7] has proved the existence of a weak solution provided that Uo(x ) is ...
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The symmetric doubly stochastic inverse eigenvalue problem (hereafter SDIEP) is to determine the necessary and sufficient conditions for an $n$-tuple $sigma=(1,lambda_{2},lambda_{3},ldots,lambda_{n})in mathbb{R}^{n}$ with $|lambda_{i}|leq 1,~i=1,2,ldots,n$, to be the spectrum of an $ntimes n$ symmetric doubly stochastic matrix $A$. If there exists an $ntimes n$ symmetric doubly stochastic ...
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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2011
ISSN: 0022-0396
DOI: 10.1016/j.jde.2010.09.025