Homotopy Regularization for a High-Order Parabolic Equation
Sign Up to like & getrecommendations! Published in 2019 at "Mediterranean Journal of Mathematics"
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
L2-norm blow-up of solutions to a fourth order parabolic PDE involving the Hessian
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Differential Equations"
DOI: 10.1016/j.jde.2018.06.015
Abstract: Abstract This paper deals with a fourth order parabolic PDE arising in the theory of epitaxial growth of crystal. We focalize the study on one open question proposed by Escudero et al. (2015) [4] ,… read more here.
Keywords: fourth order; order parabolic; parabolic pde; norm blow ... See more keywords
The second-order parabolic PDEs with singular coefficients and applications
Sign Up to like & getrecommendations! Published in 2020 at "Stochastic Analysis and Applications"
DOI: 10.1080/07362994.2020.1766983
Abstract: Abstract The goal of this paper is to establish the Lipschitz and estimates for a second-order parabolic PDE on with zero initial data and f satisfying a Ladyzhenskaya–Prodi–Serrin type condition. Following the theoretic result, we… read more here.
Keywords: order parabolic; applications second; second order; parabolic pdes ... See more keywords
Sharp pointwise estimates for solutions of weakly coupled second-order parabolic system in a layer
Sign Up to like & getrecommendations! Published in 2020 at "Complex Variables and Elliptic Equations"
DOI: 10.1080/17476933.2020.1797707
Abstract: ABSTRACT We deal with m-component vector-valued solutions to the Cauchy problem for a linear both homogeneous and nonhomogeneous weakly coupled second-order parabolic system in the layer . We assume that coefficients of the system are… read more here.
Keywords: order parabolic; coupled second; parabolic system; system ... See more keywords
The nonlocal inverse problem of the identification of the lowest coefficient and the right-hand side in a second-order parabolic equation with integral conditions
Sign Up to like & getrecommendations! Published in 2019 at "Boundary Value Problems"
DOI: 10.1186/s13661-019-1126-z
Abstract: In the present paper a nonlocal inverse boundary-value problem for a second-order parabolic equation is considered. This investigation introduces the identification of the lowest unknown coefficient and time-depend right-hand side in a second-order parabolic equation… read more here.
Keywords: order parabolic; inverse; parabolic equation; second order ... See more keywords
Efficient Technique for Solving (3+1)-D Fourth-Order Parabolic PDEs with Time-Fractional Derivatives
Sign Up to like & getrecommendations! Published in 2023 at "Axioms"
DOI: 10.3390/axioms12040347
Abstract: In this presented research, a hybrid technique is proposed for solving fourth-order (3+1)-D parabolic PDEs with time-fractional derivatives. For this purpose, we utilized the Elzaki integral transform with the coupling of the homotopy perturbation method… read more here.
Keywords: parabolic pdes; pdes time; time fractional; solving fourth ... See more keywords
An Analytical Technique, Based on Natural Transform to Solve Fractional-Order Parabolic Equations
Sign Up to like & getrecommendations! Published in 2021 at "Entropy"
DOI: 10.3390/e23081086
Abstract: This research article is dedicated to solving fractional-order parabolic equations using an innovative analytical technique. The Adomian decomposition method is well supported by natural transform to establish closed form solutions for targeted problems. The procedure… read more here.
Keywords: order parabolic; order; fractional order; parabolic equations ... See more keywords
Existence and Uniqueness of Generalized Solutions of Variational Inequalities with Fourth-Order Parabolic Operators in Finance
Sign Up to like & getrecommendations! Published in 2022 at "Symmetry"
DOI: 10.3390/sym14091773
Abstract: In the present study, we analyze a kind of variation-inequality problem based on symmetric structure, which also incorporates fourth-order parabolic operators with a degenerate type. The penalty method is used to construct the approximate solution… read more here.
Keywords: finance; existence uniqueness; fourth order; order parabolic ... See more keywords