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This paper deals with the analysis of a class of doubly nonlinear evolution equations in the framework of a general metric space. We propose for such equations a suitable metric formulation (which in fact extends the notion of Curve of Maximal Slope for gradient flows in metric spaces), and prove the existence of solutions for the related Cauchy problem by means of an approximation scheme by time discretization. Then, we apply our results to obtain the existence of solutions to abstract doubly nonlinear equations in reflexive Banach spaces. The metric approach is also exploited to analyze a class of evolution equations in L^1 spaces

A metric approach to a class of doubly nonlinear evolution equations and applications

SAVARE', GIUSEPPE
2008-01-01

Abstract

This paper deals with the analysis of a class of doubly nonlinear evolution equations in the framework of a general metric space. We propose for such equations a suitable metric formulation (which in fact extends the notion of Curve of Maximal Slope for gradient flows in metric spaces), and prove the existence of solutions for the related Cauchy problem by means of an approximation scheme by time discretization. Then, we apply our results to obtain the existence of solutions to abstract doubly nonlinear equations in reflexive Banach spaces. The metric approach is also exploited to analyze a class of evolution equations in L^1 spaces
2008
The Mathematics category includes resources dealing with mathematics, applied mathematics, statistics and probability.
sì
WOS:000256225900004
2-s2.0-52249103512
Esperti anonimi
Inglese
Internazionale
STAMPA
7
1
97
169
73
The Mathematical Citation Quotient (MSQ) for 2007 of ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA. CLASSE DI SCIENZE is 0.81 (to be compared with 0.26, the 2007 All Journal MCQ). MCQ is an index provided by the American Mathematical Society http://www.ams.org/mathscinet/help/citation_database_help_full.html#journalinfo Its Impact Factor (2007) is 0.692. Founded in 1871 initially in order to publish the best undergraduate theses and graduate dissertations of the Normale along with sporadic outside contributions. In 1932, under the direction of Leonida Tonelli the Annali became a journal of pure and applied mathematics. Published quarterly, it became famous internationally and published articles of great importance in the history of mathematics After a brief pause due to the war and the death of Tonelli, the Annali began their third period in 1947 under the direction of Alessandro Faedo and became increasingly international in scope. In 1974 Guido Stampacchia became the director and the 4 th series was begun, with a selection committee for the articles to be published and increasing rigor. Edoardo Vesentini, editor from 1978, and then Enrico Arbarello widened the subjects areas of the Annali, making it more interdisciplinary; its international fame grew considerably. A 5 th series was begun in 2002 under the direction of Giuseppe Tomassini. Currently available in all main scientific libraries, especially abroad, it is published in four volumes a year. The authors are generally foreign and the language usually English. Selection of articles is always entrusted to referee chosen from among experts in each field.
Doubly nonlinear equations; Analysis in metric spaces; Existence and approximation results; Gradient flows
sì
3
info:eu-repo/semantics/article
262
Rossi, R; Mielke, A; Savare', Giuseppe
1 Contributo su Rivista::1.1 Articolo in rivista
none
1.1 Articolo in rivista
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11571/116537
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