Search results
Results from the WOW.Com Content Network
In mathematics, a weak solution (also called a generalized solution) to an ordinary or partial differential equation is a function for which the derivatives may not all exist but which is nonetheless deemed to satisfy the equation in some precisely defined sense. There are many different definitions of weak solution, appropriate for different ...
In a weak formulation, equations or conditions are no longer required to hold absolutely (and this is not even well defined) and has instead weak solutions only with respect to certain "test vectors" or "test functions". In a strong formulation, the solution space is constructed such that these equations or conditions are already fulfilled.
A weak base is a base that, upon dissolution in water, does not dissociate completely, so that the resulting aqueous solution contains only a small proportion of hydroxide ions and the concerned basic radical, and a large proportion of undissociated molecules of the base.
The stability of solutions in holds as follows: a locally uniform limit of a sequence of solutions (or subsolutions, or supersolutions) is a solution (or subsolution, or supersolution). More generally, the notions of viscosity sub- and supersolution are also conserved by half-relaxed limits.
Ritz–Galerkin method (after Walther Ritz) typically assumes symmetric and positive definite bilinear form in the weak formulation, where the differential equation for a physical system can be formulated via minimization of a quadratic function representing the system energy and the approximate solution is a linear combination of the given set ...
Any feasible solution to the primal (minimization) problem is at least as large as any feasible solution to the dual (maximization) problem. Therefore, the solution to the primal is an upper bound to the solution of the dual, and the solution of the dual is a lower bound to the solution of the primal. [1] This fact is called weak duality.
It’s not about that solution. It is about being as fearless as one can, and behaving as beautifully as one can, under completely impossible circumstances.” Prince Harry quotes Toni Morrison # ...
The weak maximum principle, in this setting, says that for any open precompact subset M of the domain of u, the maximum of u on the closure of M is achieved on the boundary of M. The strong maximum principle says that, unless u is a constant function, the maximum cannot also be achieved anywhere on M itself.