Existence and blow‐up studies of a p(x)‐Laplacian parabolic equation with memory
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DOI: 10.1002/mma.7144
Abstract: In this paper, we establish existence and finite time blow up of weak solutions of a parabolic equation of p(x)-Laplacian type with the Dirichlet boundary condition. Moreover, we obtain upper and lower bounds for the… read more here.
Keywords: parabolic equation; blow studies; studies laplacian; existence blow ... See more keywords
Recovering the source term for parabolic equation with nonlocal integral condition
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DOI: 10.1002/mma.7331
Abstract: The main purpose of this article is to present a Tikhonov method to construct the source function f(x) of the parabolic diffusion equation. This problem is well known to be severely ill‐posed. Therefore, regularization is… read more here.
Keywords: parabolic equation; term parabolic; recovering source; equation ... See more keywords
Homotopy Regularization for a High-Order Parabolic Equation
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DOI: 10.1007/s00009-019-1424-9
Abstract: In this work we study the solvability of the Cauchy Problem for a quasilinear degenerate high-order parabolic equation \begin{equation*} \left\{ \begin{tabular}{lcl} $u_t=(-1)^{m-1}\nabla\cdot(f^n(|u|)\nabla\Delta^{m-1}u)$ & &in $\mathbb{R}^N\times\mathbb{R}_+$, $u(x,0)=u_0(x)$& & in $\mathbb{R}^N$, \end{tabular} \right. \end{equation*} with $m\in\mathbb{N},\ m>1$… read more here.
Keywords: order parabolic; parabolic equation; high order; regularization ... See more keywords
Blow-Up Phenomena for a Class of Parabolic or Pseudo-parabolic Equation with Nonlocal Source
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DOI: 10.1007/s00009-021-01735-3
Abstract: In this paper, we consider a class of parabolic or pseudo-parabolic equation with nonlocal source term: $$\begin{aligned} u_t-\nu \triangle u_t-\hbox {div}(\rho (|\nabla u|)^2\nabla u)=u^p(x,t)\int _{\Omega }k(x,y)u^{p+1}(y,t)dy, \end{aligned}$$ where $$\nu \ge 0$$ and $$p>0$$ . Using… read more here.
Keywords: pseudo parabolic; equation nonlocal; class parabolic; parabolic equation ... See more keywords
Existence and Uniqueness of an Inverse Memory Kernel for an Integro-Differential Parabolic Equation with Free Boundary
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DOI: 10.1007/s10883-017-9372-9
Abstract: We consider an inverse problem for an integro-differential parabolic equation with free boundary. This inverse problem aims to identify the memory kernel function from a global measurement data. Based on a fixed point argument, we… read more here.
Keywords: parabolic equation; integro differential; differential parabolic; memory kernel ... See more keywords
The Quenching Behavior for a Quasilinear Parabolic Equation with Singular Source and Boundary Flux
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DOI: 10.1007/s10883-018-9415-x
Abstract: In this paper, we consider the quenching behavior for a one-dimensional quasilinear parabolic equation with singular source and boundary flux. We show that the quenching occurs only on the boundary in finite time, and derive… read more here.
Keywords: singular source; parabolic equation; source boundary; quasilinear parabolic ... See more keywords
On the well-posedness of a nonlinear pseudo-parabolic equation
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DOI: 10.1007/s11784-020-00813-5
Abstract: In this paper we consider the Cauchy problem for the pseudo-parabolic equation: $$\begin{aligned} \dfrac{\partial }{\partial t} \left( u + \mu (-\Delta )^{s_1} u\right) + (-\Delta )^{s_2} u = f(u),\quad x \in \Omega ,~ t>0. \end{aligned}$$… read more here.
Keywords: well posedness; pseudo parabolic; posedness nonlinear; parabolic equation ... See more keywords
Time-discretization schema for a semilinear pseudo-parabolic equation with integral conditions
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DOI: 10.1016/j.apnum.2019.09.002
Abstract: Abstract In this paper, we use the Rothe time-discretization method to prove the existence and uniqueness of a strong solution of a semilinear pseudo-parabolic equation with integral conditions. We also provided an example to illustrate… read more here.
Keywords: pseudo parabolic; parabolic equation; time discretization; semilinear pseudo ... See more keywords
Strong solutions to a parabolic equation with linear growth with respect to the gradient variable
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DOI: 10.1016/j.jde.2018.01.050
Abstract: Abstract In this paper we prove existence and uniqueness of strong solutions to the homogeneous Neumann problem associated to a parabolic equation with linear growth with respect to the gradient variable. This equation is a… read more here.
Keywords: parabolic equation; equation linear; growth respect; strong solutions ... See more keywords
Well-posedness problem of an anisotropic parabolic equation
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DOI: 10.1016/j.jde.2019.08.014
Abstract: Abstract In this paper, we are concerned with well-posedness of an anisotropic parabolic equation with the convection term. When some diffusion coefficients are degenerate on the boundary ∂Ω and the others are positive on Ω… read more here.
Keywords: parabolic equation; anisotropic parabolic; problem anisotropic; well posedness ... See more keywords
Homogenization of parabolic equation in an evolving domain with an oscillating boundary
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2018.03.063
Abstract: Abstract In this article, we study the existence, uniqueness and homogenization of the heat equation in a domain with highly oscillating and evolving (time-dependent) boundary and an inhomogeneous time-dependent data on the oscillating part of… read more here.
Keywords: parabolic equation; equation evolving; evolving domain; homogenization parabolic ... See more keywords