Blow-Up in a Fourth-Order Semilinear Parabolic Equation From . . .

Five Types of Blow-up in a Semilinear Fourth-order Reaction-diffusion Equation: an Analytic-numerical Approach

Five types of blow-up patterns that can occur for the 4th-order semilinear parabolic equation of reaction-diffusion type ut = −∆2u+ |u|p−1u in R × (0, T ), p > 1, limt→T− supx∈RN |u(x, t)| = +∞, are discussed. For the semilinear heat equation ut = ∆u+ u , various blow-up patterns were under scrutiny since 1980s, while the case of higher-order diffusion was studied much less, regardless a wide r...

Life Span of Blow-up Solutions for Higher-order Semilinear Parabolic Equations

In this article, we study the higher-order semilinear parabolic equation ut + (−∆)u = |u|, (t, x) ∈ R+ × R , u(0, x) = u0(x), x ∈ R . Using the test function method, we derive the blow-up critical exponent. And then based on integral inequalities, we estimate the life span of blow-up solutions.

On a Spectrum of Blow-up Patterns for a Higher-order Semilinear Parabolic Equation

Blow-up in a fourth-order semilinear parabolic equation from explosion-convection theory

with a parameter β 0, which is a model equation from explosion-convection theory. Unlike the classical Frank-Kamenetskii equation ut = uxx+e u (a solid fuel model), by using analytical and numerical evidence, we show that the generic blow-up in this fourth-order problem is described by a similarity solution u∗(x, t) = − ln(T − t) + f1(x/(T − t)) (T > 0 is the blowup time), with a non-trivial pr...

Some Blow-Up Problems For A Semilinear Parabolic Equation With A Potential

The blow-up rate estimate for the solution to a semilinear parabolic equation ut = ∆u+V (x)|u|p−1u in Ω×(0, T ) with 0-Dirichlet boundary condition is obtained. As an application, it is shown that the asymptotic behavior of blow-up time and blow-up set of the problem with nonnegative initial data u(x, 0) = Mφ(x) as M goes to infinity, which have been found in [5], are improved under some reason...