Displaying similar documents to “Existence of solutions for an elliptic-algebraic system describing heat explosion in a two-phase medium”

existence of solutions for an elliptic-algebraic system describing heat explosion in a two-phase medium

Cristelle Barillon, Georgy M. Makhviladze, Vitaly A. Volpert (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Similarity:

The paper is devoted to analysis of an elliptic-algebraic system of equations describing heat explosion in a two phase medium filling a star-shaped domain. Three types of solutions are found: classical, critical and multivalued. Regularity of solutions is studied as well as their behavior depending on the size of the domain and on the coefficient of heat exchange between the two phases. Critical conditions of existence of solutions are found for arbitrary positive source function. ...

Heat kernel estimates for critical fractional diffusion operators

Longjie Xie, Xicheng Zhang (2014)

Studia Mathematica

Similarity:

We construct the heat kernel of the 1/2-order Laplacian perturbed by a first-order gradient term in Hölder spaces and a zero-order potential term in a generalized Kato class, and obtain sharp two-sided estimates as well as a gradient estimate of the heat kernel, where the proof of the lower bound is based on a probabilistic approach.