Consider the equation (0.1) ut = ∆u− V u+ au p in R × (0, T ); u(x, 0) = φ(x) 0, in R, where p > 1, n ≥ 2, T ∈ (0,∞], V (x) ∼ ω |x| as |x| → ∞, for some ω 6= 0, and a(x) is on the order |x| as |x| → ∞, for some m ∈ (−∞,∞). A solution to the above equation is called global if T = ∞. Under some additional technical conditions, we calculate a critical exponent p such that global solutions exist fo...

Consider the equation (0.1) ut = ∆u− V u+ au p in R × (0, T ); u(x, 0) = φ(x) 0, in R, where p > 1, n ≥ 2, T ∈ (0,∞], V (x) ∼ ω |x| as |x| → ∞, for some ω 6= 0, and a(x) is on the order |x| as |x| → ∞, for some m ∈ (−∞,∞). A solution to the above equation is called global if T = ∞. Under some additional technical conditions, we calculate a critical exponent p such that global solutions exist fo...

We study aperiodic balanced sequences over finite alphabets. A sequence v of this type is fully characterised by a Sturmian u and two constant gap y y′. show that the language eventually dendric we focus on return words to its factors. develop method for computing critical exponent asymptotic sequences, provided associated has quadratic slope. The based looking shortest bispecial factors in v. ...