Results 231 to 240 of about 332,442 (262)

Nonlinear Partial Differential Equations

2010
In this chapter we shall show how to generalise the results of the previous chapters on finite-dimensional nonlinear systems to partial differential equations. Rather than try to cover any significant part of this vast field, we shall concentrate on two problems, since the ideas then apply to many other nonlinear distributed systems. These two problems
Mi-Ho Giga, Yoshikazu Giga, Jürgen Saal
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Nonlinear Partial Differential Equations

2009
So far in this text we have been mainly concerned in applying classic methods, the Adomina decomposition method [3, 4, 5], and the variational iteration method [8, 9, 10] in studying first order and second order linear partial differential equations. In this chapter, we will focus our study on the nonlinear partial differential equations. The nonlinear
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Nonlinear Partial Differential Equations

2002
In this chapter we turn our attention to the study of the dynamical properties of solutions of nonlinear partial differential equations. We are especially interested here in those nonlinear evolutionary equations which arise in the analysis of two broad classes of partial differential equations: parabolic evolutionary equations and hyperbolic ...
George R. Sell, Yuncheng You
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Fully Nonlinear Stochastic Partial Differential Equations

SIAM Journal on Mathematical Analysis, 1996
The authors are concerned with the following stochastic partial differential equation: \[ du(t, .)= L(t, ., u, Du, D^2u) dt+ \langle b(t, .)Du+ h(t, .)u, dW(t) \rangle, \qquad u(0)= u_0, \tag{1} \] where \(L\), \(b\) and \(h\) are suitable functions and \(W\) is an \(\mathbb{R}^N\)-valued Brownian motion.
G. Da Prato, Tubaro, Luciano
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Quantum algorithms for nonlinear partial differential equations

Bulletin des Sciences Mathématiques, 2023
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Shi Jin, Nana Liu
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FOSLL* for Nonlinear Partial Differential Equations

SIAM Journal on Scientific Computing, 2015
Summary: In previous work, the first-order system LL* (FOSLL*) method was developed for linear partial differential equations. This approach seeks to minimize the residual of the equations in a dual norm induced by the differential operator, yielding approximations accurate in \(L^2(\Omega)\) rather than \(H^1(\Omega)\) or \(H(\mathrm{Div})\).
Lee, Eunjung, Manteuffel, Thomas A., Westphal, Chad R.   +2 more
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Software for Nonlinear Partial Differential Equations

ACM Transactions on Mathematical Software, 1975
The numerical solution of physically realistic nonlinear partial differential equations (PDEs) is a complicated and highly problem-dependent process which usually requires the scientist to undertake the difficult and time-consuming task of developing his own computer program to solve his problem.
Sincovec, Richard F., Madsen, Niel K.
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C-integrable nonlinear partial differential equations. III

Journal of Mathematical Physics, 1991
A technique based on a change of dependent variables, used in a previous paper to generate C-integrable nonlinear partial differential equations (PDEs) (i.e., nonlinear PDEs linearizable by an appropriate Change of variables) in 1+1 dimensions (one time and one space variables), is extended to the case of more than one space dimension. Several examples
CALOGERO, Francesco, XIAODA JI
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Attractors of Hamiltonian Nonlinear Partial Differential Equations

2021
This monograph is the first to present the theory of global attractors of Hamiltonian partial differential equations. A particular focus is placed on the results obtained in the last three decades, with chapters on the global attraction to stationary states, to solitons, and to stationary orbits.
Komech, Alexander, Kopylova, Elena
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Local solvability for nonlinear partial differential equations

Nonlinear Analysis: Theory, Methods & Applications, 2001
In the introduction we give a short survey on known results concerning local solvability for nonlinear partial differential equations; the next sections will be then devoted to the proof of a new result in the same direction. Specifically we study the semi-linear operator F(u) = P(D)u + f(x, Q 1(D)u, .., Q M(D)u) where P, Q 1, .., Q M are linear ...
F. MESSINA, RODINO, Luigi Giacomo
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