Sentence examples for be any weak solution from inspiring English sources

Let (g z)) be any weak solution of Eq. (1) such that the following properties hold.

Let (uin HW^{1,2}_{mathrm{loc}}(Omega)) be any weak solution to equation (3.6).

Let (uin HW^{1,2}_{mathrm{loc}}(Omega)) be any weak solution to linear subelliptic equations (3.1).

Let (u(x in HW^{1,2}(Omega)) be any weak solution to quasilinear subelliptic equations (1.1).

Let (u t,x)) be any weak solution of problem (5) with (phiin W_{1}), T be the maximal existence time of (u t,x)).

Let (uin HW^{1,2}(Omega)) be any weak solution to quasilinear subelliptic equations (1.1) satisfying the structural conditions H1-H3.

Assume that are positive functions and is any weak solution of (1.1)–(1.1).

Assume that ui 0(i = 1,..., n) are positive functions and (u1,..., u n ) is any weak solution of (1.1).

Let (u inmathcal{A}) be a weak solution of (1.1) in (Q_{4r}subsetOmega) for any (r>0).

(1) Let (u inmathcal{A}) be a weak solution of (1.1) in (Q_{4r}subsetOmega) for any (r>0).

A function (uin E) is said to be a (weak) solution of Eq. (1.1) if (J' u varphi=0) for any (varphiin E).