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Solution of a Goursat Problem in Optimal Domains
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Wolfgang Tutschke
Published/Copyright:
March 10, 2010
Abstract
In case a non-linear differential equation is reduced to a fixed-point problem, one has to apply a fixed-point theorem to a suitably chosen subset of the underlying function space. Generally speaking, in view of the non-linearity of the differential equation the restrictions for the data of the problem will be the more extensive the greater the chosen subset of the function space. The problem is to find an optimal subset leading to a domain of existence for the desired solution being as large as possible. The present paper will discuss this question for a Goursat problem.
Received: 2006-04-21
Published Online: 2010-03-10
Published in Print: 2007-March
© Heldermann Verlag
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Keywords for this article
Goursat problem;
Schauder fixed-point theorem;
optimal domain of existence
Articles in the same Issue
- The Cauchy Transform for the Hodge/De Rham System and Some of its Properties
- Explicit Bounds for Composition Operators Preserving BMO(ℝ)
- A Dirichlet Problem for the Inhomogeneous Polyharmonic Equation in the Upper Half Plane
- The Monomiality Approach to Multi-Index Polynomials in Several Variables
- On the Global and Local Solution of the Multidimensional Darboux Problem for Some Nonlinear Wave Equations
- Completeness Theorems for Elliptic Equations of Higher Order with Constant Coefficients
- Generating Relations of Hermite–Tricomi Functions Using a Representation of Lie Algebra 𝑇3
- Near Field Representations of the Acoustic Green's Function in a Shallow Ocean with Fluid-Like Seabed
- An Initial-Boundary Value Problem for a Viscous Compressible Flow
- On the Measurability of Additive Functionals
- On BVPS for Strongly Elliptic Systems with Higher Order Boundary Conditions
- An Example of Fractal Singular Homogenization
- Solution of a Goursat Problem in Optimal Domains
