Results 1 to 10 of about 243 (185)
Quasilinear Parabolic Equations Associated with Semilinear Parabolic Equations
Mathematics, 2023 We formulate a quasilinear parabolic equation describing the behavior of the global-in-time solution to a semilinear parabolic equation. We study this equation in accordance with the blow-up and quenching patterns of the solution to the original ...
Katsuyuki Ishii +2 more
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On weak solutions of semilinear hyperbolic-parabolic equations [PDF]
International Journal of Mathematics and Mathematical Sciences, 1996 In this paper we prove the existence and uniqueness of weak solutions of the mixed problem for the nonlinear hyperbolic-parabolic equation (K1(x,t)u′)′+K2(x,t)u′+A(t)u+F(u)=f with null Dirichlet boundary conditions and zero initial data, where F(s) is a
Jorge Ferreira
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A triviality result for semilinear parabolic equations
Mathematics in Engineering, 2022 We show a triviality result for "pointwise" monotone in time, bounded "eternal" solutions of the semilinear heat equation \begin{equation*} u_{t}=Δu + |u|^{p} \end{equation*} on complete Riemannian manifolds of dimension $n \geq 5$ with nonnegative Ricci tensor, when $p$ is smaller than the critical Sobolev exponent $\frac{n+2}{n-2}$.
Giovanni Catino +2 more
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On Comparison Principles for Parabolic Equations with Nonlocal Boundary Conditions
Boundary Value Problems, 2007 A generalization of the comparison principle for a semilinear and a quasilinear parabolic equations with nonlocal boundary conditions including changing sign kernels is obtained.
Yuandi Wang, Hamdi Zorgati
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A CARLEMAN'S INEQUALITY FOR A SYSTEM OF COUPLED PARABOLIC EQUATIONS
Pesquimat, 2014 In this work we consider a linearized system of parabolic equations associated to a semilinear system of heat equations. Following the ideas of O. Imanuvilov, M. Yamamoto and L.
Víctor Rafael Cabanillas Zannini
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Deep Neural Network Algorithms for Parabolic PIDEs and Applications in Insurance and Finance
Computation, 2022 In this paper we study deep neural network algorithms for solving linear and semilinear parabolic partial integro-differential equations with boundary conditions in high dimension. Our method can be considered as an extension of the deep splitting method
Rüdiger Frey, Verena Köck
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On a semilinear parabolic equation [PDF]
Proceedings of the American Mathematical Society, 2006 We introduce a general class of potentials V = V ( x ,
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Carleman inequality for a class of super strong degenerate parabolic operators and applications
Electronic Journal of Qualitative Theory of Differential Equations, 2023 In this paper, we present a new Carleman estimate for the adjoint equations associated to a class of super strong degenerate parabolic linear problems. Our approach considers a standard geometric imposition on the control domain, which can not be removed
Bruno Sérgio Araújo +2 more
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A Class of Semilinear Parabolic Problems and Analytic Semigroups
Mathematics, 2022 (1) Background: This paper is devoted to the study of a class of semilinear initial boundary value problems of parabolic type. (2) Methods: We make use of fractional powers of analytic semigroups and the interpolation theory of compact linear operators ...
Kazuaki Taira
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A Posteriori 𝑳∞(𝑳𝟐) and 𝑳∞(𝑯𝟏) Error Analysis of Semdiscrete Semilinear Parabolic Problems
Eurasian Journal of Science and Engineering, 2022 This paper aims to construct a posteriori error bounds for semilinear parabolic equations. The derivation of this bound is inspired by Makridakis and Nochetto 2003.
Younis A. Sabawi
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