This volume is a collection of original research papers and expository articles stemming from the scientific program of the Nonlinear PDE Emphasis Year held at Northwestern University (Evanston, IL) in March 1998. The book offers a cross-section of the most significant recent advances and current trends and directions in nonlinear partial differential equations and related topics. The book's contributions offer two perspectives. There are papers on general analytical treatment of the theory and papers on computational methods and applications originating from significant realistic mathematical models of natural phenomena. Also included are articles that bridge the gap between these two perspectives, seeking synergistic links between theory and modeling and computation. The volume offers direct insight into recent trends in PDEs. This volume is also available on the Web. Those who purchase the print edition can gain free access by going to www.ams.org/conm/
This work will serve as an excellent first course in modern analysis.
u(v – u) dé) dt = 0 for every v € KU, where p is the solution of 6 –# + Ap + ap = -kCo div (Vyu – Val" (Vy, – Va)) in Q, 6 ++bp = xCo(Ivy – Val”(Vy. – V.), a on 2, 6n A p(T) = 6Caly.(T) – ya!”(y.(T) – ya) in Q, with a =?'(yu), ...
What is U(v) if s(t) = Vt F1 – 1? . Consider the conservation law b u(x,t) da = #"a t)” – u(b, t)*]+ / g(v) day, d b di J. 1 where g is a discontinuous source term given by g(a) = 1 if a > # and g(x) = C = const if c < #.
While the development and analysis of numerical methods for linear partial differential equations is nearly complete, only few results are available in the case of nonlinear equations.
New to the Second Edition More than 1,000 pages with over 1,500 new first-, second-, third-, fourth-, and higher-order nonlinear equations with solutions Parabolic, hyperbolic, elliptic, and other systems of equations with solutions Some ...
The present book aims at presenting self-contained, state- of- the- art models of those techniques with applications to different classes of partial differential equations: transport, heat, wave and Schrödinger equations.
The book can serve and benefit mathematicians, students of, and professors of calculus, statistics, or advanced mathematics.
This book is not a textbook, but rather a coherent collection of papers from the field of partial differential equations.
Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics is the first book to provide a systematic construction of exact solutions via linear invariant subspaces for nonlinear differential ...
A massive transition of interest from solving linear partial differential equations to solving nonlinear ones has taken place during the last two or three decades.