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On an adjoint initial-boundary value problem
Differential Equations, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Nonlinear initial-boundary value problems
Nonlinear Analysis: Theory, Methods & Applications, 1987We prove global existence, uniqueness and exponential decay of a global solution, u(t), of a Cauchy problem in a Hilbert space H for an equation whose weak formulation is \[ \frac{d}{dt}(u',v)+\delta (u',v)+\alpha b(u,v)+\beta a(u,v)+(G(u),v)=0 \] where \('=d/dt\), (,) is the inner product in H, b(u,v), a(u,v) are given forms on subspaces \(U\subset W\)
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The Random Initial Boundary Value Problem
1992When dealing with Problems 1 and 2 introduced in Section 2 of Chapter 1, the physical situation to be studied can be considered as an input-output system where the set of initial and boundary conditions represent the input and the actual solution of the problem is the output and the phenomenology is modelled by a partial differential equation.
N. Bellomo, Z. Brzezniak, L. M. de Socio
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Some initial-boundary value problems
2016In this chapter we will study initial-boundary value problems and their treatment by methods of quaternionic analysis in combination with classical analytic numerical techniques. We start with a brief discussion of strategies for the treatment of time-dependent parabolic problems. Three methods should be considered here: the horizontal method of lines,
Klaus Gürlebeck +2 more
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The Cauchy problem and the initial boundary value problem in numerical relativity
Classical and Quantum Gravity, 1998Summary: Some simple ideas on numerical tractability are introduced, and are used to determine under what conditions unconstrained evolution of Einstein's field equations for the Cauchy problem is possible. The initial boundary value problem for Einstein's equations is discussed and a precise description of what boundary data are needed is given ...
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Initial-Boundary Value Problems for Linear Hyperbolic System
SIAM Review, 1986This paper is primarily a survey of theory developed in the early and mid 1970's by H. O. Kreiss and others. The theory discussed deals with boundary-initial value problems for linear first order hyperbolic systems. A brief discussion is given in one space dimension. Here it is shown that boundary conditions may not be chosen arbitrarily since portions
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The Initial-Boundary Value Problem and the Constraint
2013In this chapter we introduce the definitions of boundary data and of constraints. More precisely, we study the initial-boundary value problem in Sect. 6.2, the constrained Riemann problem in Sect. 6.3, the constrained Cauchy problem in Sect. 6.4 and finally the constrained initial-boundary value problem in the last section.
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