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Existence of weak solutions for abstract hyperbolic-parabolic equations [PDF]
International Journal of Mathematics and Mathematical Sciences, 1994 In this paper we study the Existence and Uniqueness of solutions for the following Cauchy problem:A2u″(t)+A1u′(t)+A(t)u(t)+M(u(t))=f(t), t∈(0,T) (1)u(0)=u0; A2u′(0)=A212u1; where A1 and A2 are bounded linear operators in a ...
Marcondes Rodrigues Clark
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Stability of Stochastic Partial Differential Equations
Axioms, 2023 In this paper, we study the stability of the stochastic parabolic differential equation with dependent coefficients. We consider the stability of an abstract Cauchy problem for the solution of certain stochastic parabolic differential equations in a ...
Allaberen Ashyralyev, Ülker Okur
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MHD Equations in a Bounded Domain
Annales Mathematicae Silesianae, 2021 We consider the MHD system in a bounded domain Ω ⊂ ℝN, N = 2; 3, with Dirichlet boundary conditions. Using Dan Henry’s semigroup approach and Giga–Miyakawa estimates we construct global in time, unique solutions to fractional approximations of the MHD ...
Kania Maria B.
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On a nonlocal problem for parabolic equation with time dependent coefficients
Advances in Difference Equations, 2021 This paper is devoted to the study of existence and uniqueness of a mild solution for a parabolic equation with conformable derivative. The nonlocal problem for parabolic equations appears in many various applications, such as physics, biology. The first
Nguyen Duc Phuong +3 more
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Boundary Value Problems, 2018 This paper is concerned with a kind of first-order quasilinear parabolic partial differential equations associated with a class of ordinary differential equations with two-point boundary value problems. We prove that the function given by the solution of
Ning Ma, Zhen Wu
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Nonexistence results of solutions of parabolic-type equations and systems on the Heisenberg group
Boundary Value Problems, 2023 In this paper, we present necessary conditions for the existence of weak solution of the parabolic-type equations and systems on the Heisenberg group. The main technique for proving the results relies on the method of test functions.
Wei Shi
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Boundary Value Problems, 2019 In this paper, we present a reduced high-order compact finite difference scheme for numerical solution of the parabolic equations. CFDS4 is applied to attain high accuracy for numerical solution of parabolic equations, but its computational efficiency ...
Baozou Xu, Xiaohua Zhang
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Boundary Value Problems, 2020 The aim of this paper is to show some applications of Sobolev inequalities in partial differential equations. With the aid of some well-known inequalities, we derive the existence of global solution for the quasilinear parabolic equations.
Yuanfei Li, Lianhong Guo, Peng Zeng
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Analysis of non scalar control problems for parabolic systems by the block moment method
Comptes Rendus. Mathématique, 2023 This article deals with abstract linear time invariant controlled systems of parabolic type. In [9], with A. Benabdallah, we introduced the block moment method for scalar control operators.
Boyer, Franck, Morancey, Morgan
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Scientific Reports, 2021 The quest for high-performance of heat transfer components on the basis of accommodating shapes, smaller weights, lower costs and little volume has significantly diverted the industries for the enhancement of heat dissipation with variable thermal ...
Basma Souayeh, Kashif Ali Abro
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