On Parabolic Equations for Measures

On Parabolic Equations for Measures

Nonautonomous Parabolic Equations Involving Measures

where Ω ⊂ R and Γ is the boundary of Ω. In this case μΩ is a bounded Radon measure on Ω× J and μΓ is such a measure on Γ× J . In [10] the semilinear analogues of (0.1) and (0.2), where μ and (μΩ, μΓ), respectively, may also depend nonlinearly and nonlocally on the unknown solution u, are investigated. Based on the results of [5], general existence, uniqueness, and continuity theorems are proved...

Parabolic equations for measures on infinite-dimensional spaces

In a series of papers [1]–[4] we considered parabolic equations for measures on R. Our motivation was a study of the Kolmogorov equations for transition probabilities of diffusion processes. Here we are concerned with similar problems in infinite dimensions. Applications are given to stochastic partial differential equations such as stochastic equations of Navier– Stokes and reaction-diffusion ...

Nonautonomous Parabolic Equations Involving Measures H

In the first part of this paper, we study abstract parabolic evolution equations involving Banach space-valued measures. These results are applied in the second part to second-order parabolic systems under minimal regularity hypotheses on the coefficients. DOI: https://doi.org/10.1007/s10958-005-0376-8 Posted at the Zurich Open Repository and Archive, University of Zurich ZORA URL: https://doi....

Uniqueness of solutions to weak parabolic equations for measures

We study uniqueness of parabolic equations for measures μ(dtdx) = μt(dx)dt of the type L∗μ = 0, satisfying μt → ν as t→ 0, where each μt is a probability measure on Rd, L = ∂t + aij(t, x)∂xi∂xj + bi(t, x)∂xj is a differential operator on (0, T ) × Rd and ν is a given initial measure. One main result is that uniqueness holds under uniform ellipticity and Lipschitz conditions on aij but for bi me...