On Parabolic Equations for Measures

A note on critical point and blow-up rates for singular and degenerate parabolic equations

In this paper, we consider singular and degenerate parabolic equations$$u_t =(x^alpha u_x)_x +u^m (x_0,t)v^{n} (x_0,t),quadv_t =(x^beta v_x)_x +u^q (x_0,t)v^{p} (x_0,t),$$ in $(0,a)times (0,T)$, subject to nullDirichlet boundary conditions, where $m,n, p,qge 0$, $alpha, betain [0,2)$ and $x_0in (0,a)$. The optimal classification of non-simultaneous and simultaneous blow-up solutions is determin...

A new positive definite semi-discrete mixed finite element solution for parabolic equations

In this paper, a positive definite semi-discrete mixed finite element method was presented for two-dimensional parabolic equations. In the new positive definite systems, the gradient equation and flux equations were separated from their scalar unknown equations.  Also, the existence and uniqueness of the semi-discrete mixed finite element solutions were proven. Error estimates were also obtaine...

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....

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 ...

WELL- POSEDNESS OF THE ROTHE DIFFERENCE SCHEME FOR REVERSE PARABOLIC EQUATIONS

Parameter determination in a parabolic inverse problem in general dimensions

It is well known that the parabolic partial differential equations in two or more space dimensions with overspecified boundary data, feature in the mathematical modeling of many phenomena. In this article, an inverse problem of determining an unknown time-dependent source term of a parabolic equation in general dimensions is considered. Employing some transformations, we change the inverse prob...