Results 41 to 50 of about 242 (185)
Numerical Methods for Partial Differential Equations, Volume 42, Issue 5, September 2026.ABSTRACT In this work, we present an extension of the semi‐discrete Lagrangian‐Eulerian numerical scheme for diffusive‐dispersive conservation law problems, including a jump discontinuous flux function. As in the one‐dimensional scalar hyperbolic case, the no‐flow curves also organize the geometry of the method.
Eduardo Abreu +2 more
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Boundary Value Problems, 2017 This paper deals with a semilinear parabolic equation with variable source under the case that the initial energy is less than the potential well depth. We deduce a sharp threshold for blow-up and global existence of solutions.
Jinge Yang, Haixiong Yu
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Well‐posedness of heat equations with nonlinearities of arbitrarily rapid growth
Proceedings of the London Mathematical Society, Volume 133, Issue 3, September 2026.Abstract We address local‐ and global‐in‐time well‐posedness of the Cauchy problem for nonlinear heat equations without imposing growth rate restrictions on the nonlinearity a priori. Our results constitute a nontrivial expansion of the classical Lq$L^q$‐theory for nonlinearities dominated by polynomial growth and the exponential‐Orlicz space theory ...
Yohei Fujishima +2 more
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Semilinear Parabolic Equations, Diffusions, and Superdiffusions
Journal of Functional Analysis, 1998 This paper deals with first and second initial-boundary value problems of the heat equation in a bounded domain lying in \(\mathbb{R}^{n+1}\) with \(L^p\) boundary data. The author defines certain mixed (thermal) potentials in terms of the fundamental solution for the heat equation.
openaire +2 more sources
Well‐Posedness and Analyticity of Solutions to the Stationary MHD Equations
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Volume 106, Issue 8, August 2026.ABSTRACT We consider the stationary problem of the MHD equations in R3$\mathbb {R}^3$. The aim of this article is to show existence, uniqueness, regularity, and analyticity of solutions in the scaling invariant homogeneous Besov space Ḃp,q−1+3/p$\dot{B}^{-1 + 3/p}_{p, q}$ for 1⩽p<3$1 \leqslant p < 3$ and 1⩽q⩽∞$1 \leqslant q \leqslant \infty$.
Kento Sube
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Numerical Investigation of a Diffusive SIR Model: Focus on Positivity Preservation
Mathematical Methods in the Applied Sciences, Volume 49, Issue 11, Page 11775-11793, 30 July 2026.ABSTRACT In this paper, we consider a system of semilinear partial differential equations (PDEs) representing a spatially extended SIR epidemic model. A brief analytical investigation of the well‐posedness and positivity of the solutions is provided in the appendix, while the main focus is on the numerical treatment of the model.
Rahele Mosleh +2 more
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A cell complex structure for the space of heteroclines for a semilinear parabolic equation
Electronic Journal of Differential Equations, 2009 It is well known that for many semilinear parabolic equations there is a global attractor which has a cell complex structure with finite dimensional cells.
Michael Robinson
doaj
Existence and Uniqueness of Nonmonotone Solutions in Porous Media Flow
Axioms, 2022 Existence and uniqueness of solutions for a simplified model of immiscible two-phase flow in porous media are obtained in this paper. The mathematical model is a simplified physical model with hysteresis in the flux functions.
Rouven Steinle +3 more
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Spreading Speed for a Vector‐Borne Disease System on Non‐Coincident Straight Infinite Cylinders
Studies in Applied Mathematics, Volume 156, Issue 6, June 2026.ABSTRACT Vector‐borne diseases remain an increasing global public health concern. In this work, we investigate the spreading speed of vector‐borne disease via a four‐component reaction–diffusion system posed on non‐coincident straight infinite cylinders, which stands for an unconventional spatial configuration.
Arnaud Ducrot +2 more
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Global weak solutions for the compressible Poisson–Nernst–Planck–Navier–Stokes system
Journal of the London Mathematical Society, Volume 113, Issue 5, May 2026.Abstract We consider the compressible Poisson–Nernst–Planck–Navier–Stokes (PNPNS) system of equations, governing the transport of charged particles under the influence of the self‐consistent electrostatic potential, in a three‐dimensional bounded domain.
Daniel Marroquin, Dehua Wang
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