The phrase "a regular solution of" is correct and usable in written English.
It is typically used in mathematical or scientific contexts to refer to a solution that satisfies certain regularity conditions or properties.
Example: "In this study, we will explore a regular solution of the differential equation that models the system's behavior."
Alternatives: "a standard solution to" or "a typical solution for".
In a regular solution of composition x1 and x2, the probability that the neighbour of a given molecule is of species 1 is given by the mole fraction x1, and the probability that it is of species 2 is given by x2.
Let u ( x, t ) be a regular solution of (1 -(4).
If the vector function satisfies ( 1.1 ) almost everywhere in, then it is called a regular solution of ( 1.1 ).
If for any, there exists a regular solution of ( 1.1 ) which satisfies boundary condition ( 1.2 ) in the sense that (14).
We will seek the solution of the boundary value problem (2.1), (2.2) in the form (u(t)=v(t)+u_{0}(t)), where (u_{0}(t)) is a regular solution of problem (3.23), (3.24).
Definition 1.1 If the vector function u ( t ) ∈ W 2 3 ( R + ; H ) satisfies equation (1.1) almost everywhere in R +, then it is called a regular solution of equation (1.1).
Roughly speaking, the open-loop solvability is equivalent to the solvability of a forward-backward stochastic differential equation (FBSDE, for short), and the closed-loop solvability is equivalent to the existence of a regular solution to a Riccati equation.
In particular, it is useful to distinguish between two types of limiting behaviour: one corresponds to that of a regular solution; the other, to that of an athermal solution (i.e., when components are mixed, no heat is generated or absorbed).
Properties of a regular solution are best examined based on the concept of excess function[16].
Under these conditions, we prove the existence of a unique regular solution of this problem.
Then for any function f ∈ C 1 , there exists a unique regular solution of the Problem B.
