This article deals with the Cauchy problem for a forward–backward parabolic equation, which is of interest in physical and biological models. Considering such an equation as the singular limit of an appropriate pseudoparabolic third-order regu- larization, we consider the framework of entropy solutions, namely weak solutions satisfying an additional entropy inequality inherited by the higher order equation. Moreover, we restrict the attention to two-phase solutions, that is solutions taking values in the intervals where the parabolic equation is well-posed, proving existence and uniqueness of such solutions.
Two-phase entropy solutions of a forward-backward parabolic equation / Mascia, Corrado; Terracina, Andrea; Tesei, Alberto. - In: ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS. - ISSN 0003-9527. - STAMPA. - 194:(2009), pp. 887-925. [10.1007/s00205-008-0185-6]
Two-phase entropy solutions of a forward-backward parabolic equation
MASCIA, Corrado;TERRACINA, Andrea;TESEI, Alberto
2009
Abstract
This article deals with the Cauchy problem for a forward–backward parabolic equation, which is of interest in physical and biological models. Considering such an equation as the singular limit of an appropriate pseudoparabolic third-order regu- larization, we consider the framework of entropy solutions, namely weak solutions satisfying an additional entropy inequality inherited by the higher order equation. Moreover, we restrict the attention to two-phase solutions, that is solutions taking values in the intervals where the parabolic equation is well-posed, proving existence and uniqueness of such solutions.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.