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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Peano Type Theorem for Abstract Parabolic Equations [PDF]
Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2009 We consider parabolic problems with non-Lipschitz nonlinearity in the different scales of Banach spaces and prove local-in-time existence theorem.
Zubelevich, Oleg
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Shadowing for discrete approximations of abstract parabolic equations
Discrete & Continuous Dynamical Systems - B, 2008 This paper is devoted to the numerical analysis of abstract semilinear parabolic problems $u'(t) = Au(t) + f(u(t)), u(0)=u^0,$ in some general Banach space $E$. We prove a shadowing Theorem that compares solutions of the continuous problem with those of a semidiscrete approximation (time stays continuous) in the neighborhood of a hyperbolic ...
W. Beyn, S. Piskarev
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Stabilization of solutions of abstract parabolic equations [PDF]
Czechoslovak Mathematical Journal, 1980 J. Kacur
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Evolution operators for higher order abstract parabolic equations [PDF]
Czechoslovak Mathematical Journal, 1986 The author shows the existence of an evolution operator for a higher order abstract parabolic equation with variable coefficients. The techniques employed are similar to Tanabe's method [\textit{H. Tanabe}, Osaka Math. J. 12, 363-376 (1960; Zbl 0098.313)].
E. Obrecht
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Application of Rothe's method to abstract parabolic equations [PDF]
Czechoslovak Mathematical Journal, 1974 J. Necas
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Bi-spaces global attractors in abstract parabolic equations [PDF]
Banach Center Publications, 2003 J. Cholewa, Tomasz Dłotko
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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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Maximum bound principles for a class of semilinear parabolic equations and exponential time differencing schemes [PDF]
SIAM Review, 2020 The ubiquity of semilinear parabolic equations has been illustrated in their numerous applications ranging from physics, biology, to materials and social sciences.
Q. Du, L. Ju, Xiao Li, Zhonghua Qiao
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On quasilinear parabolic evolution equations in weighted Lp-spaces II [PDF]
, 2013 Our study of abstract quasi-linear parabolic problems in time-weighted L_p-spaces, begun in [17], is extended in this paper to include singular lower order terms, while keeping low initial regularity.
D. Bothe +6 more
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