Numerical solution of the problem on reconstructing the initial condition for a semilinear parabolic equation

2006 ◽  
Vol 21 (4) ◽  
Author(s):  
E. I. Parmuzin ◽  
V. P. Shutyaev
Keyword(s):  
Parabolic Equation ◽  
Numerical Solution ◽  
Semilinear Parabolic Equation ◽  
Initial Condition ◽  
Semilinear Parabolic

scholarly journals A SUFFICIENT CONDITION FOR SLOW DECAY OF A SOLUTION TO A SEMILINEAR PARABOLIC EQUATION

2012 ◽  
Vol 10 (04) ◽  
pp. 363-371 ◽  
Author(s):  
I. BEN ARBI ◽  
A. HARAUX
Keyword(s):  
Parabolic Equation ◽  
Connected Domain ◽  
Neumann Boundary ◽  
Semilinear Parabolic Equation ◽  
Sufficient Condition ◽  
Initial Condition ◽  
Absolute Value ◽  
Slow Decay ◽  
Bounded Smooth ◽  
Semilinear Parabolic

We consider the equation ψt - Δψ + c|ψ|p-1ψ = 0 with Neumann boundary conditions in a bounded smooth open connected domain of ℝn with p > 1, c > 0. We show that if the initial condition is small enough and if the absolute value of its average overpasses a certain multiple of the pth power of its L∞ norm, then ψ(t, ⋅) decreases like [Formula: see text].

scholarly journals Measure Control of a Semilinear Parabolic Equation with a Nonlocal Time Delay

2018 ◽  
Vol 56 (6) ◽  
pp. 4434-4460
Author(s):  
Eduardo Casas ◽  
Mariano Mateos ◽  
Fredi Tröltzsch
Keyword(s):  
Parabolic Equation ◽  
Time Delay ◽  
Semilinear Parabolic Equation ◽  
Semilinear Parabolic

scholarly journals The Problem of Determining of the Source Function and of the Leading Coefficient in the Many-dimensional Semilinear Parabolic Equation

2001 ◽  
Vol 14 (4) ◽  
pp. 497-506
Author(s):  
Svetlana V. Polyntseva ◽  
◽  
Kira I. Spirina
Keyword(s):  
Inverse Problem ◽  
Parabolic Equation ◽  
Existence And Uniqueness ◽  
Source Function ◽  
Time Interval ◽  
Semilinear Parabolic Equation ◽  
Existence And Uniqueness Theorem ◽  
Bounded Functions ◽  
The Many ◽  
Semilinear Parabolic

We consider the problem of determining the source function and the leading coefficient in a multidimensional semilinear parabolic equation with overdetermination conditions given on two different hypersurfaces. The existence and uniqueness theorem for the classical solution of the inverse problem in the class of smooth bounded functions is proved. A condition is found for the dependence of the upper bound of the time interval, in which there is a unique solution to the inverse problem, on the input data

scholarly journals First Boundary Value Problem for Cordes-Type Semilinear Parabolic Equation with Discontinuous Coefficients

2020 ◽  
Vol 2020 ◽  
pp. 1-4
Author(s):  
Aziz Harman ◽  
Ezgi Harman
Keyword(s):  
Parabolic Equation ◽  
Parabolic Equations ◽  
Discontinuous Coefficients ◽  
Semilinear Parabolic Equation ◽  
Semilinear Parabolic Equations ◽  
Strong Solvability ◽  
Carathéodory Function ◽  
The Subject ◽  
Cordes Condition ◽  
Semilinear Parabolic

For a class of semilinear parabolic equations with discontinuous coefficients, the strong solvability of the Dirichlet problem is studied in this paper. The problem ∑i,j=1naijt,xuxixj−ut+gt,x,u=ft,x,uΓQT=0, in QT=Ω×0,T is the subject of our study, where Ω is bounded C2 or a convex subdomain of En+1,ΓQT=∂QT\∖t=T. The function gx,u is assumed to be a Caratheodory function satisfying the growth condition gt,x,u≤b0uq, for b0>0,q∈0,n+1/n−1,n≥2, and leading coefficients satisfy Cordes condition b0>0,q∈0,n+1/n−1,n≥2.

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