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On the numerical study of nonlinear initial-boundary value problems or initial-value problems
Applied Mathematics and Computation, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zaki F. A. El-Reheem, A. H. Nasser
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On the initial boundary value problem for a shallow water equation
Journal of Mathematical Physics, 2004In this paper, we obtain the existence and uniqueness of the local strong solutions to the initial boundary problem for a one-dimensional shallow-water equation (Camassa–Holm equation) on the half-space {x>0} with initial data uo∈H2(R+)∩H01(R+). The solution is obtained as a limit of the solutions for a class of approximation problems.
Ma, Shixiang, Ding, Shijin
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Initial-Boundary Value and LC Problems
2013Evaluation of European-style derivatives can be reduced to solving initial value or initial-boundary value problems of parabolic partial differential equations. This chapter discusses numerical methods for such problems. If an American option problem is formulated as a linear complementarity problem, then the only difference between solving a European ...
You-lan Zhu +3 more
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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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Initial-boundary value problems on the sphere
2016In this chapter, we consider classes of fluid flow problems on the sphere and in ball shells with given initial and boundary value conditions. We focus our attention on the corresponding Navier-Stokes equations and their linearizations – the socalled forecasting equations.
Klaus Gürlebeck +2 more
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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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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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