arXiv subjects

Michaela Zahradníková

Publications and source records attributed to Michaela Zahradníková.

4 recordsLinked to original sources

arXiv2026

Traveling waves for combustion reaction-diffusion-convection equations: the full range of wave speeds

We consider traveling wave solutions to a reaction--diffusion--convection equation with a combustion-type reaction term. While a necessary condition for the existence of traveling waves is $c \geq H^*:=\sup_{0<u \leq θ} \big(-\frac{1}{u} \int_0^u h(σ)\,dσ\big)$, where $c$ denotes the wave speed, $θ\in(0,1)$ the ignition threshold, and $h$ the convective term, the available results in \cite{DZ25,MM03} establish existence and nonexistence only under the restriction $c \geq -\min_{u\in[0,1]} h(u)$. In this note, we close this gap by covering the entire range $c\ge H^*$.

math.AP↗

arXiv2026

Traveling waves for bistable reaction-diffusion-convection equations with discontinuous density-dependent coefficients

Continuing our previous study \cite{DJKZ} on the monostable reaction-diffusion-convection equation, we analyze the bistable case under weak regularity assumptions. Our approach applies monostable results on the subintervals where the reaction term $g$ has constant sign, thereby establishing both existence and nonexistence of bistable traveling wave solutions. We extend the results of \cite{MMM04}, obtained for $p=2$ under higher regularity assumptions ($d \in C^1[0,1]$, $g,h \in C[0,1]$), to the $p$-Laplacian with $p>1$ in our weak regularity setting.

math.AP↗

arXiv2026

Traveling waves for monostable reaction-diffusion-convection equations with discontinuous density-dependent coefficients

This paper concerns wave propagation in a class of scalar reaction-diffusion-convection equations with $p$-Laplacian-type diffusion and monostable reaction. We introduce a new concept of a non-smooth traveling wave profile, which allows us to treat discontinuous diffusion with possible degenerations and singularities at 0 and 1, as well as only piecewise continuous convective velocity. Our approach is based on comparison arguments for an equivalent non-Lipschitz first-order ODE. We formulate sufficient conditions for the existence and non-existence of these generalized solutions and discuss how the convective velocity affects the minimal wave speed compared to the problem without convection. We also provide brief asymptotic analysis of the profiles, for which we need to assume power-type behavior of the diffusion and reaction terms.

math.AP↗

arXiv2024

Traveling waves in reaction-diffusion-convection equations with combustion nonlinearity

This paper concerns the existence and properties of traveling wave solutions to reaction-diffusion-convection equations on the real line. We consider a general diffusion term involving the $p$-Laplacian and combustion-type reaction term. We extend and generalize the results established for $p=2$ to the case of singular and degenerate diffusion. Our approach allows for non-Lipschitz reaction as well. We also discuss the shape of the traveling wave profile near equilibria, assuming power-type behavior of the reaction and diffusion terms.

math.AP↗