REGULARIZATION OF QUASILINEAR HEAT EQUATIONS BY A FRACTIONAL NOISE

2004 ◽  
Vol 04 (02) ◽  
pp. 201-221 ◽  
Author(s):  
DAVID NUALART ◽  
YOUSSEF OUKNINE
Keyword(s):  
Parabolic Equation ◽  
White Noise ◽  
Existence And Uniqueness ◽  
Integrability Condition ◽  
Quasilinear Parabolic Equation ◽  
One Dimension ◽  
Heat Equations ◽  
Fractional Noise ◽  
Uniqueness Of A Solution ◽  
Quasilinear Parabolic

We show the existence and uniqueness of a solution for a quasilinear parabolic equation in one dimension driven by an additive fractional white noise, assuming that the drift is measurable and satisfies a suitable integrability condition. The proof is based on Girsanov theorem and lower estimates of the density of the solution of the equation without drift.

scholarly journals Blow-Up Analysis for a Quasilinear Parabolic Equation with Inner Absorption and Nonlinear Neumann Boundary Condition

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Zhong Bo Fang ◽  
Yan Chai
Keyword(s):  
Boundary Condition ◽  
Parabolic Equation ◽  
Neumann Boundary Condition ◽  
Blow Up ◽  
Quasilinear Parabolic Equation ◽  
Neumann Boundary ◽  
Initial Boundary ◽  
Blow Up Analysis ◽  
Inner Absorption ◽  
Quasilinear Parabolic

We investigate an initial-boundary value problem for a quasilinear parabolic equation with inner absorption and nonlinear Neumann boundary condition. We establish, respectively, the conditions on nonlinearity to guarantee thatu(x,t)exists globally or blows up at some finite timet*. Moreover, an upper bound fort*is derived. Under somewhat more restrictive conditions, a lower bound fort*is also obtained.

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