Displaying similar documents to “The Method of Lines for Nonlinear Parabolic Differential Equations with Mixed Derivatives.”

Some Nonlinear Evolution Problems in Mixed Form

Ulisse Stefanelli, Augusto Visintin (2009)

Bollettino dell'Unione Matematica Italiana

Similarity:

This work deals with some abstract equations, either linear or nonlinear, arising from the so-called mixed formulation of PDEs of elliptic and parabolic type. This class of variational formulations turns out to be particularly relevant in connection with the development of finite elements approximations. We prove the well-posedness of both the stationary and the evolution problems.

Existence of explosive solutions to some nonlinear parabolic Itô equations

Pao-Liu Chow (2015)

Banach Center Publications

Similarity:

The paper is concerned with the problem of existence of explosive solutions for a class of nonlinear parabolic Itô equations. Under some sufficient conditions on the initial state and the coefficients, it is proven by the method of auxiliary functionals that there exist explosive solutions with positive probability. The main results are presented in Theorems 3.1 and 3.2 under different sets of conditions. An example is given to illustrate some application of the second theorem. ...