In mathematics, a weak solution (also called a generalized solution) to an ordinary or partial differential equation is a function for which the derivatives...

simple enough to remember (e.g., Maharajah and the Sepoys). An ultra-weak solution (e.g., Chomp or Hex on a sufficiently large board) generally does not...

example for a weak solution is as follows: ϕ ( x ) = 1 4 π 1 | x | {\displaystyle \phi (x)={\frac {1}{4\pi }}{\frac {1}{|x|}}} is a weak solution satisfying...

}fv\,dx.} This is what is usually called the weak formulation of Poisson's equation. Functions in the solution space V {\displaystyle V} must be zero on...

present, in solution, in equilibrium with each other. HA ⇌ H+ + A− Acetic acid (CH3COOH) is an example of a weak acid. The strength of a weak acid is quantified...

Weak Hero (Korean: 약한영웅) is a South Korean television series written and directed by Yoo Soo-min with Kim Jin-seok and Park Dan-hee, starring Park Ji-hoon...

continuous, then there exists a unique solution u ∈ H 0 1 ( Ω ) {\displaystyle u\in H_{0}^{1}(\Omega )} to the weak problem (*). If further A ( u , φ ) {\displaystyle...

classical solution satisfying the PDE in regular sense, so we search for a weak solution at first, and then find out whether the weak solution is smooth...

with prescribed boundary conditions (boundary value problems), where weak solutions may not be regular enough to satisfy the boundary conditions in the...

acts as a buffer in the ocean. Buffer solutions resist pH change because of a chemical equilibrium between the weak acid HA and its conjugate base A−: HA...

Tincture of iodine, iodine tincture, or weak iodine solution is an antiseptic. It is usually 2% elemental iodine, along with potassium iodide or sodium...

at 14%, 20 °C. Stoichiometric solutions are fairly alkaline, with pH 11 or higher since the hypochlorite ion is a weak base: OCl− + H2O ⇌ HOCl + OH− The...

(defined below), one can define a type of weak solution called viscosity solution. Under the viscosity solution concept, u does not need to be everywhere...

always less than or equal to the solution to the dual minimization problem. So, in short: weak duality states that any solution feasible for the dual problem...

diffuses through the membrane without reacting, methanol is fed as a weak solution: this decreases efficiency significantly, since crossed-over methanol...

characteristic of an aqueous strong electrolyte solution; the solutes in a weaker electrolyte solution are present as ions, but only to a small degree...

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...

bilinear form can be "inverted" to show the existence and uniqueness of a weak solution to a given boundary value problem. The result was proved by J Necas...

lemma and Fredholm alternative, states the sufficient condition for a weak solution u to exist in the Sobolev space Hk. For example, for a Second-order...

products of functions also hold for the weak derivative. This concept gives rise to the definition of weak solutions in Sobolev spaces, which are useful for...

the solution to cause the acid to remain in its protonated form. Solutions of weak acids and salts of their conjugate bases form buffer solutions. To...

as weak solutions. For example, we say that a function u belonging to the Sobolev space W 1 , p ( Ω ) {\displaystyle W^{1,p}(\Omega )} is a weak solution...

what constitutes a solution to the SDE. There are two main definitions of a solution to an SDE, a strong solution and a weak solution Both require the existence...

equilibrium of solutions of sodium hydroxide at higher concentrations must also be considered. A weak acid or the conjugate acid of a weak base can be treated...

weak. The properties of electrolytes may be exploited using electrolysis to extract constituent elements and compounds contained within the solution.[citation...

unconditional existence and uniqueness for weak solutions of the harmonic map heat flow. Moreover, he found that his weak solutions are smooth away from finitely many...

3-dimensional Navier–Stokes equations is not known to hold for weak solutions, since a weak solution u {\displaystyle u} is only known to satisfy u ∈ L 2 ( [...

In mathematics, a function f {\displaystyle f} is weakly harmonic in a domain D {\displaystyle D} if ∫ D f Δ g = 0 {\displaystyle \int _{D}f\,\Delta g=0}...

paper with a weak solution of ordinary table salt (sodium chloride), blotting and drying it, then brushing one side with a strong solution of silver nitrate...

derivative, T is the matrix transpose, and I is the identity matrix. A weak solution of this system is defined to be an element f of the Sobolev space W1...