Abstract
The Critical Curves of a Doubly Nonlinear Parabolic Equation in Non-divergent form with a Source and Nonlinear Boundary Flux
Highlights
Introduction and main resultsThis work studies the critical curves of a degenerate parabolic equation with doubly nonlinearity in non-divergence form with a source ( ) ∂u = uk ∂ ∂t∂x um−1 ∂u p−2 ∂u ∂x ∂x + uβ,(x, t) ∈ R+ × (0; +∞) . (1)Initial condition and nonlinear boundary condition are−um−1 ∂u p−2 ∂u (0, t) = uq (0, t), t ∈ (0; +∞), (2)
Let us consider the following globally defined in time supersolution in the self-similar form u (t, x)
Let us consider a blow-up solution of the Cauchy problem
Summary
Where p > 2, m 1, q, β > 0, 0 k < 1 are given parameters and u0 (x) is bounded, nontrivial, nonnegative and continuous function. The main objective of this work is to define the critical curves and the region of parameters where global solutions and blow-up solutions exist. Any solution of problem (1)–(3) blows up in finite time. Rg = {β > p (1 − k) + k + m + p − 2, q > p (1 − k) + (k + m + p − 3)} , there exist both global and blow-up solutions of problem (1)–(3). Let us consider the following globally defined in time supersolution in the self-similar form u (t, x) eLt Let us consider a blow-up solution of the Cauchy problem. Let β < 1 and the following self-similar subsolution of problem (5) has the form u (x, t) = tαφ (ξ) , ξ = xt−γ,.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
