We study the mixed Dirichlet–Neumann problem for Laplace equation in complement of a bounded convex polygonal quadrilateral extended complex plane. The Dirichlet / Neumann conditions at opposite pairs sides are $$\{0,1\}$$ and $$\{0,0\},$$ resp. solution to this is harmonic function unbounded polygon known as potential quadrilateral. compute values u including its value infinity. main result pa...

In this paper, we consider singular and degenerate parabolic equations$$u_t =(x^alpha u_x)_x +u^m (x_0,t)v^{n} (x_0,t),quadv_t =(x^beta v_x)_x +u^q (x_0,t)v^{p} (x_0,t),$$ in $(0,a)times (0,T)$, subject to nullDirichlet boundary conditions, where $m,n, p,qge 0$, $alpha, betain [0,2)$ and $x_0in (0,a)$. The optimal classification of non-simultaneous and simultaneous blow-up solutions is determin...

In this paper, we shall give examples to answer that an open problem posed by De Baets et al. in “Triangular norms on product lattices (Fuzzy Sets and Systems 104(1999), 61-75)”.