990 resultados para SCALAR FIELD-EQUATIONS
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12, no. 1
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12, no. 3
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v.16(1923)
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n.s. no.36(2003)
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v.7:no.4(1912)
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no.4(1922)
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v.37:no.4(1977)
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v.21:no.3(1935)
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v.32(1973)
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v. 42 (1971)
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v. 41 (1970)
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v. 44 (1973)
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We consider linear stochastic differential-algebraic equations with constant coefficients and additive white noise. Due to the nature of this class of equations, the solution must be defined as a generalised process (in the sense of Dawson and Fernique). We provide sufficient conditions for the law of the variables of the solution process to be absolutely continuous with respect to Lebesgue measure.
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We review several results concerning the long time asymptotics of nonlinear diffusion models based on entropy and mass transport methods. Semidiscretization of these nonlinear diffusion models are proposed and their numerical properties analysed. We demonstrate the long time asymptotic results by numerical simulation and we discuss several open problems based on these numerical results. We show that for general nonlinear diffusion equations the long-time asymptotics can be characterized in terms of fixed points of certain maps which are contractions for the euclidean Wasserstein distance. In fact, we propose a new scaling for which we can prove that this family of fixed points converges to the Barenblatt solution for perturbations of homogeneous nonlinearities for values close to zero.