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Monotone Operators In Banach Space And Nonlinear Partial Differential Equations Pdf

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This book is concerned with basic results on Cauchy problems associated with nonlinear monotone operators in Banach spaces with applications to partial differential equations of evolutive type. This is a monograph about the most significant results obtained in this area in last decades but is also written as a graduate textbook on modern methods in partial differential equations with main emphasis on applications to fundamental mathematical models of mathematical physics, fluid dynamics and mechanics. Skip to main content Skip to table of contents.

• Nonlinear Differential Equations of Monotone Types in Banach Spaces
• PUBLICATIONS
• Monotone Operators in Banach Space and Nonlinear Partial Differential Equations - E-bog

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Nonlinear Differential Equations of Monotone Types in Banach Spaces

Augusto VisintiN. Auchmuty , Saddle-points and existence-uniqueness for evolution equations, Differential Integral Equations , 6 , Google Scholar. Baiocchi and A. Wang , The kernel average for two convex functions and its applications to the extension and representation of monotone operators, Trans. Brezis and I.

PUBLICATIONS

Metrics details. Without assuming the existence of upper-lower solutions or compactness or continuity conditions, we prove the unique existence of a positive fixed point and also construct two iterative schemes to approximate it. As applications, we research a nonlinear fractional differential equation with multi-point fractional boundary conditions. By using the obtained fixed point theorems of sum-type operator, we get the sufficient conditions which guarantee the existence and uniqueness of positive solutions. At last, a specific example is provided to illustrate our result. With a significant development and extensive applications in various differential and integral equations, nonlinear operators theory has been an active area of research in nonlinear functional analysis. Over the past several decades, much attention has been paid to various fixed point theorems for the single nonlinear operator, and a lot of important results have been obtained, see for example [ 1 — 10 ].

The objectives of this monograph are to present some topics from the theory of monotone operators and nonlinear semigroup theory which are directly applicable to the existence and uniqueness theory of initial-boundary-value problems for partial differential equations and to construct such operators as realizations of those problems in appropriate function spaces. A highlight of this presentation is the large number and variety of examples introduced to illustrate the connection between the theory of nonlinear operators and partial differential equations. These include primarily semilinear or quasilinear equations of elliptic or of parabolic type, degenerate cases with change of type, related systems and variational inequalities, and spatial boundary conditions of the usual Dirichlet, Neumann, Robin or dynamic type. The discussions of evolution equations include the usual initial-value problems as well as periodic or more general nonlocal constraints, history-value problems, those which may change type due to a possibly vanishing coefficient of the time derivative, and other implicit evolution equations or systems including hysteresis models. The scalar conservation law and semilinear wave equations are briefly mentioned, and hyperbolic systems arising from vibrations of elastic-plastic rods are developed.

Skip to search form Skip to main content You are currently offline. Some features of the site may not work correctly. DOI: Showalter Published Mathematics. PDE examples by type Linear problems An introduction Nonlinear stationary problems Nonlinear evolution problems Accretive operators and nonlinear Cauchy problems Appendix Bibliography Index.

This is an example of how an a-priori estimate and continuity lead to the existence of a solution to a nonlinear equation, f(x) = 0. We shall obtain such results in the.

Monotone Operators in Banach Space and Nonlinear Partial Differential Equations - E-bog

In this chapter we present the basic theory of maximal monotone operators in reflexive Banach spaces along with its relationship and implications in convex analysis and existence theory of nonlinear elliptic boundary value problems. However, the latter field is not treated exhaustively but only from the perspective of its implications to nonlinear dynamics in Banach spaces. Unable to display preview. Download preview PDF. Skip to main content.

The existence and uniqueness results of entropy solutions are established. Full text available only in PDF format.

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